Question

In: Statistics and Probability

A particular fruit's weights are normally distributed, with a mean of 218 grams and a standard...

A particular fruit's weights are normally distributed, with a mean of 218 grams and a standard deviation of 18 grams.

If you pick one fruit at random, what is the probability that it will weigh between 257 grams and 273 grams

Expert Solution

Solution :

Given that ,

mean = = 218

standard deviation = = 18

n = 1

= 218

= / $\sqrt$ n= 18 / $\sqrt$ 1=18

P(257< < 273) = P[(257-218) / 18< ( - ) / < (273-218) /18 )]

= P( -2.17< Z <3.06)

= P(Z <3.06 ) - P(Z < -2.17)

Using z table

=0.9989-0.015

=0.9839

probability= 0.9839

orchestra answered 2 years ago

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