Question

A particular fruit's weights are normally distributed, with a mean of 228 grams and a standard deviation of 13 grams. If you pick one fruit at random, what is the probability that it will weigh between 207.2 grams and 218.9 grams?

(If you get two values that are the same, please regenerate the problem or contact the instructor if you are unable to do so.)

Answer =  (Round to four decimal places.)

Warning: Do not use the Z Normal Tables...they may not be accurate enough since WAMAP may look for more accuracy than comes from the table.

Answer 1

Let, X be the fruit's weight

mean of fruit's weight = m = 228 grams

standard deviation of fruit's weight = s = 13 grams

We need to find the probability that it will weigh between 207.2 grams and 218.9 grams or P[ 207.2 < X < 218.9 ]

P[ 207.2 < X < 218.9 ] = P[ ( 207.2 - m )/s < ( X - m )/s < ( 218.9 - m )/s ]

P[ 207.2 < X < 218.9 ] = P[ ( 207.2 - 228 )/13 < ( X - 228 )/13 < ( 218.9 - 228 )/13 ]

P[ 207.2 < X < 218.9 ] = P[ -1.6 < Z < -0.7 ]

P[ 207.2 < X < 218.9 ] = P[ Z < -0.7 ] - P[ Z < -1.6 ]

P[ 207.2 < X < 218.9 ] = 0.472097 - 0.436441 = 0.035656

P[ 207.2 < X < 218.9 ] = 0.035656

P[ 207.2 < X < 218.9 ] = 0.0356 ( rounded off to two decimal places )