Question

Typhoid fever is more common in developing countries with poor sanitation and greater incidence of food contamination. The mean duration of this illness is approximately 4 weeks. Periodically, a team of doctors randomly selects 10 patients with typhoid fever and carefully measures the duration of the illness. If the mean duration is greater than 4.5 weeks, then a health alert is issued. Suppose the duration of this illness is normally distributed with standard deviation 1 week.

Fill in the blanks. (Give your answers to four decimal places.)

1. The probability that the sample mean duration is less than 4.5 weeks is _(Answer 1) _.
2. The probability that a health alert is issued is _(Answer 2) _.
3. Suppose the true mean duration has increased to 4.3 weeks. The probability that a health alert will be issued is _(Answer 3) _.

Answer 1

Given that, mean = 4 week and

standard deviation = 1 week

Q.1) We want to find,

Therefore, the probability that the sample mean duration is less than 4.5 weeks is 0.9429

Q.2) We want to find,

Therefore, the probability that a health alert is issued is 0.0571

Q.3) Suppose the true mean duration has increased to 4.3 weeks. That is, suppose, mean = 4.3

We want to find,

Therefore, the probability that a health alert will be issued is 0.2643