A particular fruit's weights are normally distributed, with a mean of 422 grams and a standard...

A particular fruit's weights are normally distributed, with a mean of 422 grams and a standard deviation of 35 grams. If you pick one fruit at random, what is the probability that it will weigh between 386 grams and 541 grams

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Expert Solution

Solution :

Given that ,

mean = = 422

standard deviation = = 35

n = 1

= 422

= / $\sqrt$ n= 35 / $\sqrt$ 1=35

P(386< <541 ) = P[(386-422) /35 < ( - ) / < (541-422) /35 )]

= P( -1.03< Z <3.4 )

= P(Z <3.4 ) - P(Z <-1.03 )

Using z table

=0.9997-0.1515

=0.8482

probability=0.8482

orchestra answered 1 year ago

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