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?

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

Step-by-step 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%)