Use the NORM.S.DIST () function to calculate the following probabilities, X ~ N(100, 25): (a) P(X ≤ 95); (b) P(95 ≤ X ≤ 105); (c) P(105 ≤ X ≤ 115); and (d) P(93 ≤ X ≤ 99). In each case convert X to Z....

Use the NORM.S.DIST () function to calculate the following probabilities, X ~ N(100, 25): (a) P(X ≤ 95); (b) P(95 ≤ X ≤ 105); (c) P(105 ≤ X ≤ 115); and (d) P(93 ≤ X ≤ 99). In each case convert X to Z. Compare with your answers from Exercise X4.1.

Q56

Given that a normal variable has a mean of 10 and a variance of 25, calculate the probability that a member chosen at random is: (a) ≥ 11, (b) ≤ 11, (c) ≤ 5, (d) ≥ 5, (e) between 5 and 11.

The lifetimes of certain types of car battery are normally distributed with a mean of 1248 days and standard deviation of 185 days. If the supplier guarantees them for 1080 days, what proportion of batteries will be replaced under guarantee?