Question

What is the probability that a random sample of 14 pregnancies has a mean gestation period of less than 196 ​days? The probability that the mean of a random sample of 14 pregnancies is less than 196 days is approximately . ​(Round to four decimal places as​ needed.)

Answer 1

here we should use standard normal variate z=(x-mean)/(sd/sqrt(n))

for x=196 the z=(196-mean)/(sd/sqrt(14))=z1(let)

now we find P(X<196)=P(Z<z1) and we get the required probability. so here we need the value of mean and standard deviation(sd).

let if mean=201 and standard deviation=17 then

z=(196-201)/(17/sqrt(24))=-1.4409

so P(X<196)=P(Z<1.4409)=0.0748 ( using ms-excel =normsdist(-1.4408))

please provide the mean and standard deviation for the quality of answer