A particular fruit's weights are normally distributed, with a mean of 652 grams and a standard...

A particular fruit's weights are normally distributed, with a mean of 652 grams and a standard deviation of 22 grams. If you pick 7 fruit at random, what is the probability that their mean weight will be between 624 grams and 637 grams

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Expert Solution

Solution :

Given that ,

mean = = 652

standard deviation = = 22

n = 7

= 652

= / $\sqrt$ n= 22 / $\sqrt$ 7=8.3

P(624< <637 ) = P[(624-652) /8.3 < ( - ) / < (637-652) /8.3 )]

= P(-3.37 < Z <-1.81 )

= P(Z <-1.81 ) - P(Z < -3.37)

Using z table

=0.0351 - 0.0004

=0.0347

probability= 0.0347

orchestra answered 1 year ago

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