Question

a certain tropical fruit has weights that are normally distributed, with a mean of 521 grams and a standard deviation of 12 grams. If you pick 15 fruits at random, what is the probability that the mean weight of the sample will be between 520 grams and 521 grams? Round your answer to three decimal places.

Answer 1

Solution :

Given that,

mean = = 521

standard deviation = = 12

n = 15

= 521

= / n = 12 / 15 = 3.0984

P(520 < < 521) = P((520 - 521) / 3.0984 < ( - ) / < (521 - 521) / 3.0984))

= P(-0.323 < Z < 0)

= P(Z < 0) - P(Z < -0.323)

= 0.5 - 0.3733

= 0.1267

= 0.127

Probability = 0.127