Question

A particular fruit's weights are normally distributed, with a mean of 678 grams and a standard deviation of 6 grams.

If you pick 18 fruit at random, what is the probability that their mean weight will be between 675 grams and 676 grams? Round answer to at least 4 decimal places.

Answer 1

P(675 < < 676)

= 678

= 6

  

P(-2.121 < z < -1.414)

The probability that −2.121<Z<−1.414 is equal to the blue area under the curve.

P (−2.121<Z<−1.414 ) = P ( Z<−1.414 )−P (Z<−2.121 )

P ( Z < −1.414)=1−P ( Z<1.414 ) = 1−0.9207 = 0.0793

P ( Z<−2.121)=1−P ( Z<2.121 )=1−0.983=0.017

Hence,

P (−2.121 < Z < −1.414 ) = 0.0623