Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=162 days and standard deviation σ=10 days.

Complete parts​ (a) through​ (f) below.

​(a) What is the probability that a randomly selected pregnancy lasts less than

159 days?The probability that a randomly selected pregnancy lasts less than 159 days is approximately .3821

(Round to the nearest integer as​ needed.)

A.If 100 pregnant individuals were selected independently from this​ population, we would expect ___pregnancies to last more than 159 days.

Answer 1

Let

X~N(u,sigma²)

mean(u)=162.

Sigma=10

Que(a) What is the probability that a randomly selected pregnancy lasts less than 159 days?

Solutions→

Z= (x-u)/sigma

Prob(x<159)

= Prob [(z<(159-162)/10]

=Prob[z<-0.3]

=0.3821

Que(b)   If 100 pregnant individuals were selected independently from this​ population, we would expect ___pregnancies to last more than 159 days.

Solutions→

Sample size n= 100

Let p1→pregenacy last more than 159 days

Prob(xbar>159)

=Prob[(xbar-u)/(sigma/√n)>(159-162)/(10/√100)]

=Prob[Z > -3]

=0.9987

P1= 0.9987*100=99.87≈100

Almost all 100 pregnancy last more tha 159 days.

Thanks!