Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean p = 180 days and standard deviation o = 11 days. Complete parts (a) through (f) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) What is the probability that a randomly selected pregnancy lasts less than 176 days? The probability that a randomly selected pregnancy lasts less than 176 days is approximately 1. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 176 days. O B. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last exactly 176 days. OC. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last less than 176 days. (b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x is with Hz = and o=0. (Round to four decimal places as needed.) (c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 176 days or less? The probability that the mean of a random sample of 17 pregnancies is less than 176 days is approximately (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 independent random samples of size n= 17 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 176 days or more. OB. If 100 independent random samples of size n= 17 pregnancies were obtained from this population, we would expect OC. If 100 independent random samples of size n=17 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 176 days. sample(s) to have a sample mean of 176 days or less. (d) What is the probability that a random sample of 52 pregnancies has a mean gestation period of 176 days or less? The probability that the mean of a random sample of 52 pregnancies is less than 176 days is approximately (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 independent random samples of size n= 52 pregnancies were obtained from this population, we would expect OB. If 100 independent random samples of size n = 52 pregnancies were obtained from this population, we would expect OC. If 100 independent random samples of size n = 52 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of 176 days or more. sample(s) to have a sample mean of 176 days or less. sample(s) to have a sample mean of exactly 176 days.

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	180
std deviation   =σ=	11.000

a)

probability =P(X<176)=(Z<(176-180)/11)=P(Z<-0.36)=0.3594

option C is correct: and filler is 36

b)

the sampling distribution of xbar is approximately normal with μx=180 and σx=σ/√n=2.6679

c)

probability =P(X<176)=(Z<(176-180)/2.668)=P(Z<-1.5)=0.0668

option C is correct: and filler is 7

d)

probability =P(X<176)=(Z<(176-180)/1.525)=P(Z<-2.62)=0.0044

option B is correct :   and filler is 0

e) .....would be unusual.........is less than 180 days

f)

probability =P(171<X<189)=P((171-180)/2.84)<Z<(189-180)/2.84)=P(-3.17<Z<3.17)=0.9992-0.0008=0.9984