The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of $112 and a standard deviation of $9. Which of the following is the answer for the probability that the next individual who buys a product will make a purchase of more than $116?
A) 71%
B) 48%
C) 33%
D) 42%

Question

Quizplus · Accepted Answer

To find the probability that the next individual will make a purchase of more than $116, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question ($116), μ is the mean ($112), and σ is the standard deviation ($9). Plugging in the numbers, we get Z = (116 - 112) / 9 = 4 / 9 ≈ 0.44. Looking up 0.44 on the standard normal distribution table or using a calculator, we find that the area to the left of Z = 0.44 is approximately 0.67, meaning 67% of the data falls below $116. Therefore, the probability of a purchase being more than $116 is 1 - 0.67 = 0.33 or 33%.

The Ransin Sports Company Has Noted That the Size of Individual