Question

D Question 9 9 pts The average age of all doctors is 42.0 years old with a standard deviation of 11.0 years. If 16 doctors are chosen at random for a committee, find the probability that the mean age of those doctors is less than 43.50 years.

Answer 1

Let X be the average age of doctors

X~ N (42, 11)

So according to central limit theorem

$\bar x \sim N(42,\frac{11}{\sqrt{16}}) \\ \\ i.e. \bar x \sim N(42,\frac{11}{4}) \\ \\ \bar x \sim N(42,2.75)$

Required probability

$=P(\bar x < 43.5)$

$=P(Z < \frac{43.5-42}{2.75})$

Answer: 0.7073

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