1. Which one of the following probabilities are incorrect with regard to a standard normal distribution?

• A.P(Z ? 0.5) = 0.3085
• B.P( Z ? 0.5) = P( Z ? -0.5)
• C.P(Z ? 0.5) = 1 - P(Z ? 0.5)
• D.P(-0.5 ? Z ? 0.5) = P(Z ? 0.5) - P(Z ? -0.5)
• E.P(Z = 0.5) = 0.0000

2. A random variable X is normally distributed with a mean of 85 and a standard deviation of 20. Calculate the probability that X is at most 125 and choose the answer from the options below.

A.0.9938

B. 0.8413

C. 0.9772

D. 0.6915

E. 0.9332

3.

Analytics from online meeting tools shows an average meeting duration of 90 minutes. Assume the average meeting duration is the population mean, the popuiation standard deviation is 90 and that a random sample of 90 online meetings are selected. it is further known that the probability that the average meeting duration is long is 0.2981 i.e. PO? 2 x) = 0.2981. Calculate the value of x and choose the correct answer from the options below to determine when the meeting is long