Question

Question 25)

A particular fruit's weights are normally distributed, with a mean of 771 grams and a standard deviation of 28 grams.

If you pick 5 fruit at random, what is the probability that their mean weight will be between 750 grams and 779 grams

Answer 1

Solution :

Given that,

mean = = 771

standard deviation = = 28

n = 5

= 771

= / n =28 / 5 = 12.52

P(750< <779 )  

= P[(750 -771) /12.52 < ( - ) / < (778 -771) /12.52 )]

= P(-1.68 < Z <0.56 )

= P(Z <0.56 ) - P(Z <- 1.68 )

Using z table,  

= 0.7078 -0.0375

= 0.6703