The second dose of the COVID-19 vaccine is more likely to produce side effects than the first. The time between receiving the shot and the onset of side effects is called the lag time. According to one study, the lag times (among the subjects that reported side effects from a second dose of the vaccine) were normally distributed with a mean of 14 hours, with a standard deviation of 3 hours.

(a) What is the probability that a person selected at random from among those that experienced side effects from their second dose of the vaccine had a lag time of less than 11 hours?

(b) What is the probability that a person selected at random from among those that experienced side effects from their second dose of the vaccine had a lag time between 14 and 20 hours?

(c) Estimate a range of lag times, centered about the mean, that should include about 95% of all lag times for those experiencing side effects.

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