Normal Distribution Question

Question

A particular fruit's weights are normally distributed, with a mean of 614 grams and a standard deviation of 16 grams.

If you pick one fruit at random, what is the probability that it will weigh between 560 grams and 635 grams. (Give answer to 4 decimal places.)

Answer 1

x = fruit weight

We want to find P(560 < x < 635) using standardized normal probability table

standardized normal z-score = (x - mean)/std

Translate above inequality to use standardized table:

P( (560 - 614)/16 < z < (635-614)/16)

P(-3.375 < z < 1.3125)

P(z < 1.3125) - P(z < -3.375) = 0.905 - 0 = 0.905