A particular fruit's weights are normally distributed, with a mean of 318 grams and a standard deviation of 37 grams. If you pick one fruit at random, what is the probability that it will weigh between 256 grams and 433 grams

P(256 ≤ x ≤ 433) = 0.951

Step-by-step explanation:

Since the weights of the fruit are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = weights of fruit.

µ = mean weight

σ = standard deviation

From the information given,

µ = 318 grams

σ = 37 grams

the probability that a fruit selected at random will weigh between 256 grams and 433 grams is expressed as

P(256 ≤ x ≤ 433)

For x = 256

z = (256 - 318)/37 = - 1.68

Looking at the normal distribution table, the probability corresponding to the z score is 0.048

For x = 433

z = (433 - 318)/37 = 3.1

Looking at the normal distribution table, the probability corresponding to the z score is 0.999

Therefore,

P(256 ≤ x ≤ 433) = 0.999 - 0.048 = 0.951

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