statistics help

Question

a particular fruit's weights are normal distributed, with a mean of 284 grams and a standard deviation of 7 grams.

if you pick one fruit at random, what is the probability that it will weigh between 291 grams and 306 grams?

the heaviest 7% of fruit weigh more than how many grams?

Answer 1

x = weight of fruit. N(284,7)

want P(291 < x < 306)

compute z-stat for those limits = (x - mean)/SD

P( (291-284)/7 < z < (306-284)/7) = P(1 < z < 3.14) = P(z < 3.14) - P(z < 1) = 0.9992 - 0.8413 = 0.1579

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compute z-score for 93rd percentile = 1.48

z = (x - mean)/SD

1.48 = (x - 284)/7

x = 7*1.48 + 284 = 294.36