THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4.
-What is the probability that in a particular month the office receives more than 310 orders?
A)0.7823
B)0.2826
C)0.7174
D)0.2177

Question

Quizplus · Accepted Answer

To find the probability of receiving more than 310 orders, we calculate the z-score for 310 using the formula z = (X - μ) / σ, where X is 310, μ is 298, and σ is 15.4. This gives us z = (310 - 298) / 15.4 ≈ 0.779. Looking up this z-score in a standard normal distribution table or using a calculator, we find the area to the right of this z-score is approximately 0.2177, indicating the probability of receiving more than 310 orders is 0.2177.