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!

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