Question

Farmers often sell fruits and vegetables at farmers’ markets during the summer. Each tomato stand at the Bentonville farmers’ market has a daily demand for tomatoes that is approximately normally distributed with a mean equal to 125 tomatoes per day and a standard deviation equal to 30 tomatoes per day. If a stand has 83 tomatoes available to be sold at the beginning of the day, what is the approximate probability that they will all be sold?

Answer 1

the probability that all tomatoes are sold is 0.919 (91.9%)

Explanation:

since the random variable X= number of tomatoes that are demanded, is normally distributed we can make the standard random variable Z such that:

Z=(X-μ)/σ = (83 - 125)/30 = -1.4

where μ= expected value of X= mean of X (since X is normally distributed) , σ=standard deviation of X

then all tomatoes are sold if the demand surpasses 83 tomatos , therefore

P(X>83) = P(Z>-1.4) = 1- P(Z≤-1.4)

from tables of standard normal distribution →P(Z≤-1.4)=0.081 , therefore

P(X>83) = 1- P(Z≤-1.4) = 1 - 0.081 = 0.919 (91.9%)

thus the probability that all tomatoes are sold is 0.919 (91.9%)