ps no explanations needed, just need to make sure my answers are correct. only 4 questions

1. According to a study,563% of all males between the ages of 18 and 24 live at home. (Unmarried college students living in a dorm are counted as living at home.) Suppose that a survey is administered and 155 of 244 respondents indicated that they live at home. (a) Use the normal approximation to the binomial to approximate the probability that at least 155 respondents live at home. (b) Do the results from part (a) contradict the study?

(a)P(X1515)=

(Round to four decimal places as needed.)

(b) Does the result from part (a) contradict the results of the study?

A.Yes, because the probability of P(X155) is greater than 0.05.

B.No, because the probability of P(X155) is less than 0.05.

C.Yes, because the probability of P(X155) is less than 0.05.

D.No, because the probability of P(X155) is greater than 0.05

2. Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.n=58, p=0.3, and X=21

For n=58, p=0.3, and X=21, use the binomial probability formula to find P(X).

(Round to four decimal places as needed.)

Can the normal distribution be used to approximate this probability?

A.Yes, because np(1p)10

B.No, because np(1p)10

C. Yes, because np(1p)10

D. No, because np(1p)10

Approximate P(X) using the normal distribution. Use a standard normal distribution table.

A. P(X)=

(Round to four decimal places as needed.)

B. The normal distribution cannot be used.

By how much do the exact and approximated probabilities differ?

A. = ?

(Round to four decimal places as needed.)

B. The normal distribution cannot be used.

3. Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.n=60, p=0.1, and X=15

P(X)=

(Round to four decimal places as needed.)

Can the normal distribution be used to approximate this probability?

A. No, the normal distribution cannot be used because np(1p)10.

B.Yes, the normal distribution can be used because np(1p)<10.

C. No, the normal distribution cannot be used because np(1p)<10.

D. Yes, the normal distribution can be used because np(1p)10.

Approximate P(X) using the normal distribution. Use a standard normal distribution table. Select the correct choice below and fill in any answer boxes in your choice.

A. P(X)=

(Round to four decimal places as needed.)

B. There is no solution.

By how much do the exact and approximated probabilities differ? Select the correct choice below and fill in any answer boxes in your choice.

A. =?

(Round to four decimal places as needed.)

B. There is no solution.

4. Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(x) using the normal distribution and compare the result with the exact probability. n=67, p=0.69, and x=49

For n=73, p=0.75 , and x=60

find P(x) using the binomial probability distribution.

P(x)=

(Round to four decimal places as needed.)

Can the normal distribution be used to approximate this probability?

A. Yes, the normal distribution can be used because np(1p)10.

B. Yes, the normal distribution can be used because np(1p)10.

C. No, the normal distribution cannot be used because np(1p)<10.

D. No, the normal distribution cannot be used because np(1p)10.

Approximate P(x) using the normal distribution. Select the correct choice below and fill in any answer boxes in your choice.

A. P(x)=

(Round to four decimal places as needed.)

B. The normal distribution cannot be used to approximate the binomial distribution in this case.

Compare the normal approximation with the exact probability. Select the correct choice below and fill in any answer boxes in your choice.

A.The exact probability is greater than the approximated probability by =?.

(Round to four decimal places as needed.)

B.The exact probability is less than the approximated probability by =?.

(Round to four decimal places as needed.)

C.The exact and approximated probabilities are equal.

D. The normal distribution cannot be used to approximate the binomial distribution in this case.