Answer: 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
