Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

- Suppose
*n*= 31 and *p*= 0.36.

(For each answer, enter a number. Use 2 decimal places.)*n*·*p* = *n*·*q* =

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank

both *n*·*p* and *n*·*q* exceed

fourth blank (Enter an exact number.)

What are the values of μ_{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)

μ_{p̂} = mu sub p hat =

σ_{p̂} = sigma sub p hat =

Suppose

*n*= 25 and*p*= 0.15.

Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank

both *n*·*p* and *n*·*q* exceed

fourth blank (Enter an exact number.)

Suppose

*n*= 63 and*p*= 0.24.

(For each answer, enter a number. Use 2 decimal places.)*n*·*p* = *n*·*q* =

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank

both *n*·*p* and *n*·*q* exceed

fourth blank (Enter an exact number.)

What are the values of μ_{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)

μ_{p̂} = mu sub p hat =

σ_{p̂} = sigma sub p hat =

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

*n*·*p* = *n*·*q* =

**Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)**

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

**first blank**

a. Yes

b. No

**second blank**

a.) can

b.) cannot

**third blank**

c.) both *n*·*p* and *n*·*q* exceed

**fourth blank (Enter an exact number.)**

______(blank)

**What are the values of μ _{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)**

μ_{p̂} = mu sub p hat =
#### (b) Suppose *n* = 25 and *p* = 0.15.

σ_{p̂} = sigma sub p hat =

**Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)**

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

**first blank**

a.) Yes

b.) No

**second blank**

a.) can

b.) cannot

**third blank**

c.) both *n*·*p* and *n*·*q* exceed

**fourth blank (Enter an exact number.)**

______(blank)

*n*·*p* = *n*·*q* =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

**first blank**

a.) Yes

b.) No

**second blank**

a.) can

b.) cannot

**third blank**

c.) both *n*·*p* and *n*·*q* exceed

**fourth blank (Enter an exact number.)**

______(blank)

μ_{p̂} = mu sub p hat =

σ_{p̂} = sigma sub p hat =

σ

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

- Suppose
*n*= 45 and *p*= 0.26.

(For each answer, enter a number. Use 2 decimal places.)*n*·*p* = *n*·*q* =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank
*n*·*p* and *n*·*q* do not exceed*n*·*q* exceeds*n*·*p*

both *n*·*p* and *n*·*q* exceed*n*·*q* does not exceed

does not exceed*n*·*p* exceeds

fourth blank (Enter an exact number.)

=#### (b)

Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

=

What are the values of μ_{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)

μ_{p̂} =

σ_{p̂} =

Suppose

*n*= 25 and*p*= 0.15.

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank
*n*·*p* and *n*·*q* do not exceed
*n*·*q* exceeds*n*·*p* does not exceed
*n*·*p* exceeds

both *n*·*p* and *n*·*q* exceed*n*·*q* does not exceed

fourth blank (Enter an exact number.)

=
#### (c)

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

Suppose

*n*= 57 and*p*= 0.24.

(For each answer, enter a number. Use 2 decimal places.)*n*·*p* = *n*·*q* =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank
*n*·*q* does not exceed
*n*·*p* and *n*·*q* do not exceed
*n*·*q* exceeds*n*·*p* does not exceed
*n*·*p* exceeds

both *n*·*p* and *n*·*q* exceed

fourth blank (Enter an exact number.)

What are the values of μ_{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)

μ_{p̂} =

σ_{p̂} =

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a) Suppose n = 42 and p = 0.37. (For each answer, enter a number. Use 2 decimal places.)

n·p =

n·q =Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

(a) Suppose n = 42 and p = 0.37. (For each answer, enter a number. Use 2 decimal places.)

n·p =

n·q =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank

both n·p and n·q exceed

n·p exceeds

n·q does not exceed

n·q exceeds

n·p does not exceed

n·p and n·q do not exceed

fourth blank (Enter an exact number.)

What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.)

μp̂ = mu sub p hat =

σp̂ = sigma sub p hat =

(b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank

both n·p and n·q exceed

n·p exceeds

n·q does not exceed

n·q exceeds

n·p does not exceed

n·p and n·q do not exceed

fourth blank (Enter an exact number.)

(c) Suppose n = 62 and p = 0.32. (For each answer, enter a number. Use 2 decimal places.)

n·p =

n·q =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank

both n·p and n·q exceed

n·p exceeds

n·q does not exceed

n·q exceeds

n·p does not exceed

n·p and n·q do not exceed

fourth blank (Enter an exact number.)

What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.)

μp̂ = mu sub p hat =

σp̂ = sigma sub p hat =

(a) Suppose *n* = 29 and *p* = 0.34. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np = |

nq = |

—Select— Yes No , p̂ —Select— can cannot be approximated by a normal random variable because —Select— np and nq do not exceed nq exceeds np exceeds np does not exceed nq does not exceed both np and nq exceed .

What are the values of μ_{p̂} and σ_{p̂}? (Use 3 decimal places.)

μ_{p̂} = |

σ_{p̂} = |

(b) Suppose *n* = 25 and *p* = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not?

—Select— Yes No , p̂ —Select— can cannot be approximated by a normal random variable because —Select— nq does not exceed np exceeds both np and nq exceed np and nq do not exceed np does not exceed nq exceeds .

(c) Suppose *n* = 48 and *p* = 0.11. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np = |

nq = |

—Select— Yes No , p̂ —Select— cannot can be approximated by a normal random variable because —Select— np and nq do not exceed np exceeds nq does not exceed np does not exceed nq exceeds both np and nq exceed .

What are the values of μ_{p̂} and σ_{p̂}? (Use 3 decimal places.)

μ_{p̂} = |

σ_{p̂} = |

- Suppose
*n*= 32 and *p*= 0.39.

(For each answer, enter a number. Use 2 decimal places.)*n*·*p* = *n*·*q* =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo

second blank

cancannot

third blank

fourth blank (Enter an exact number.)

What are the values of μ_{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)

μ_{p̂} = mu sub p hat =

σ_{p̂} = sigma sub p hat =

Suppose

*n*= 25 and*p*= 0.15.

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo

second blank

cancannot

third blank

fourth blank (Enter an exact number.)

Suppose

*n*= 51 and*p*= 0.35.

(For each answer, enter a number. Use 2 decimal places.)*n*·*p* = *n*·*q* =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo

second blank

cancannot

third blank

fourth blank (Enter an exact number.)

_{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)

μ_{p̂} = mu sub p hat =

σ_{p̂} = sigma sub p hat =

(a) Suppose *n* = 25 and *p* = 0.25. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np = |

nq = |

—Select— Yes No , p̂ —Select— can cannot be approximated by a normal random variable because —Select— np exceeds nq exceeds both np and nq exceed nq does not exceed np does not exceed np and nq do not exceed .

What are the values of μ_{p̂} and σ_{p̂}? (Use 3 decimal places.)

μ_{p̂} = |

σ_{p̂} = |

(b) Suppose *n* = 25 and *p* = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not?

—Select— Yes No , p̂ —Select— can cannot be approximated by a normal random variable because —Select— nq does not exceed nq exceeds np exceeds both np and nq exceed np does not exceed np and nq do not exceed .

(c) Suppose *n* = 42 and *p* = 0.37. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np = |

nq = |

—Select— Yes No , p̂ —Select— can cannot be approximated by a normal random variable because —Select— nq exceeds nq does not exceed np and nq do not exceed both np and nq exceed np does not exceed np exceeds .

What are the values of μ_{p̂} and σ_{p̂}? (Use 3 decimal places.)

μ_{p̂} = |

σ_{p̂} = |

- Suppose
*n*= 44 and *p*= 0.22.

(For each answer, enter a number. Use 2 decimal places.)*n*·*p* = *n*·*q* =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo

second blank

cancannot

third blank

fourth blank (Enter an exact number.)

_{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)

μ_{p̂} = mu sub p hat =

σ_{p̂} = sigma sub p hat =

Suppose

*n*= 25 and*p*= 0.15.

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo

second blank

cancannot

third blank

fourth blank (Enter an exact number.)

Suppose

*n*= 64 and*p*= 0.24.

(For each answer, enter a number. Use 2 decimal places.)*n*·*p* = *n*·*q* =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo

second blank

cancannot

third blank

fourth blank (Enter an exact number.)

_{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)

μ_{p̂} = mu sub p hat =

σ_{p̂} = sigma sub p hat =

- Suppose
*n*= 28 and *p*= 0.32.

(For each answer, enter a number. Use 2 decimal places.)*n*·*p* = *n*·*q* =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo

second blank

can cannot

third blank

both *n*·*p* and *n*·*q* exceed

fourth blank (Enter an exact number.)

_{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)

μ_{p̂} = mu sub p hat =

σ_{p̂} = sigma sub p hat =

Suppose

*n*= 25 and*p*= 0.15.

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo

second blank

can cannot

third blank

both *n*·*p* and *n*·*q* exceed

fourth blank (Enter an exact number.)

Suppose

*n*= 51 and*p*= 0.36.

(For each answer, enter a number. Use 2 decimal places.)*n*·*p* = *n*·*q* =

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

Yes No

second blank

can cannot

third blank

both *n*·*p* and *n*·*q* exceed

fourth blank (Enter an exact number.)

_{p̂} and σ_{p̂}? (For each answer, enter a number. Use 3 decimal places.)

μ_{p̂} = mu sub p hat =

σ_{p̂} = sigma sub p hat =

a) Suppose n = 44 and p = .22. (For each answer, enter anumber. use 2 decimal places)

n*p =

n*q =

Can we approximate *p̂* by a normal distribution?

______, *p̂* ______ be approximated by a normal random variable because ______ ______.

First blank: yes/no

Second blank: can/cannot

Third blank: n*P exceeds, n*p and n*q exceed, n*p does not exceed, n*q does not exceed, n*p and n*q do not exceed, n*q exceeds

Fourth blank: enter exact number

What are values of u*p̂* and o*p̂* ? (For each answer enter a number, use 3 decimal places)

u*p̂* =

o*p̂* =

b) Suppose n = 25 and p = 0.15. Can we safely approximate *p̂* by a normal distribution? Why or why not?

______, *p̂* ______ be approximated by a normal random variable because ______ ______.

First blank: yes/no

Second blank: can/cannot

Third blank: n*P exceeds, n*p and n*q exceed, n*p does not exceed, n*q does not exceed, n*p and n*q do not exceed, n*q exceeds

Fourth blank: enter exact number

c) Suppose n = 49 and p = 0.17 (For each answer enter a number. Use 2 decimal places)

Can we approximate *p̂* by a normal distribution? Why?

Can we approximate *p̂* by a normal distribution?

______, *p̂* ______ be approximated by a normal random variable because ______ ______.

First blank: yes/no

Second blank: can/cannot

Third blank: n*P exceeds, n*p and n*q exceed, n*p does not exceed, n*q does not exceed, n*p and n*q do not exceed, n*q exceeds

Fourth blank: enter exact number

What are values of u*p̂* and o*p̂* ? (For each answer enter a number, use 3 decimal places)

u*p̂* =

o*p̂* =

(a) Suppose *n* = 27 and *p* = 0.28. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np = |

nq = |

—Select— Yes No , p̂ —Select— cannot can be approximated by a normal random variable because —Select— np does not exceed both np and nq exceed nq does not exceed np and nq do not exceed np exceeds nq exceeds .

What are the values of μ_{p̂} and σ_{p̂}? (Use 3 decimal places.)

μ_{p̂} = |

σ_{p̂} = |

(b) Suppose *n* = 25 and *p* = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not?

—Select— Yes No , p̂ —Select— cannot can be approximated by a normal random variable because —Select— both np and nq exceed nq does not exceed np exceeds nq exceeds np does not exceed np and nq do not exceed .

(c) Suppose *n* = 41 and *p* = 0.32. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np = |

nq = |

—Select— Yes No , p̂ —Select— cannot can be approximated by a normal random variable because —Select— np exceeds nq exceeds np and nq do not exceed nq does not exceed np does not exceed both np and nq exceed .

What are the values of μ_{p̂} and σ_{p̂}? (Use 3 decimal places.)

μ_{p̂} = |

σ_{p̂} = |

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