A particular fruit's weights are normally distributed, with a mean of 515 grams and a standard...

A particular fruit's weights are normally distributed, with a mean of 515 grams and a standard deviation of 28 grams.

If you pick 4 fruit at random, what is the probability that their mean weight will be between 470 grams and 557 grams (Give answer to 4 decimal places.)

Solutions

Expert Solution

Solution :

Given that ,

mean = = 515

standard deviation = = 28

n = 4

= 515

= / $\sqrt$ n= 28 / $\sqrt$ 4=14

P(470< < 557) = P[(470-515) / 14< ( - ) / < (557-515) / 14)]

= P(-3.21 < Z <3 )

= P(Z <3 ) - P(Z <- 3.21)

Using z table

=0.9987-0.0007

=0.9980

probability=0.9980

orchestra answered 1 year ago

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