Question

A particular fruit's weights are normally distributed, with a mean of 623 grams and a standard deviation of 36 grams.

The heaviest 15% of fruits weigh more than how many grams?

Give your answer to the nearest gram.

Answer 1

Som Given XuN (u=623, 8=36) We have to find a point Á such that o & P[X> A = 0.15 2 P[XCA] = 0.80 on using using technology A = 660.3) gm 0.15 А #

Answer 2

SOLUTION :

Let a grams be the weight  over which 15% fruits are there.

P( x > a) = P( z > (a - m)/s)

=> 0.15 =  P( z > (a - m)/s)

From ND table : 

z > 1.036

The cutoff point is z = 1.036

So, 

a = z * s + m = 1.036 * 36 + 623  = 660.296 = 660 grams

So, the heaviest 15% fruits weigh more than 660 grams (ANSWER).