A normal distribution has a mean of 100 and a standard deviation of 5. Find the probability that a value selected at random is in the following interval. at most 110

Question

A normal distribution has a mean of 100 and a standard deviation of 5. Find the probability that a value selected at random is in the following interval.

at most 110

Answer 1

(110-100)/5= 10/5 = 2 standard deviations from the mean

by the empirical rule 95% fall within 2 standard deviations from the mean

1-.95 = .05 fall outside more than 2 standard deviations from the mean

.05/2 = .025 fall to the right of 2 standard deviations from the mean

.95+.025 = .975 = 97.5% will be in the interval (- infinity, 110] or at most 110

a more accurate solution is found using z tables or a z calculator

97.725%