Answer to Question #196484 in Statistics and Probability for Mbuso Zulu

Question

A sample of 50 socks is taken. What is the probability that the mean length of the sample is shorter than 18 cm?

Answer 1

$n=50, \mu=20$

$SE=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10.5}{\sqrt{50}}=\dfrac{10.5}{7.07}=1.48$

 Probability that the mean length of the sample is shorter than 18 cm is-

$P(X<18)=P(z<\dfrac{18-20}{1.48}$

$P(X<18) = P(Z < -1.35)= 0.0885$

THE PROBABILITY IS 0.0885