Question

The population of weights of a particular fruit is normally distributed, with a mean of 218 grams and a standard deviation of 19 grams. If 20 fruits are picked at random, then 5% of the time, their mean weight will be greater than how many grams? ROUND ANSWER TO NEAREST GRAM

Answer 1

Given that,

mean = = 218

standard deviation = = 19

n =  20

= 218

= / n = 19 / 20 =4.2485

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05  

= P(Z < z ) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.64) = 0.95

z = 1.64 ( using z table )

using z-score formula  

= z * +   

= 1.64 *4.2485+218

= 224.96

answer=225