Question

7. The mean weekly earnings for employees in general automotive repair shops is $450 and the standard deviation is $50. A sample of 100 automotive repair employees is selected at random.
a. Find the probability that the mean earnings is less than $445.

b. Find the probability that the mean earning is between $445 and $455.

c.Find the probability that the mean earnings is greater than $460.

8. A drug manufacturer states that only 5% of the patients using a high blood pressure drug will experience side effects. Doctors at a large university hospital use the drug in treating 200 patients.
a.What is the probability that 15 or fewer patients will experience a side effect?

b. What is the probability that between 7 and 12 patients will experience a side effect?

Answer 1

Question 7:

According to the central limit theorem, the distribution of the sample mean is given as:

a) Probability that the mean earnings is less than 445 is computed here as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get:

Therefore 0.1587 is the required probability here.

b) Probability that the mean earnings is between 445 and 455 is computed here as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.6826 is the required probability here.

c) The probability that the mean earnings is greater than 460 is computed here as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.0228 is the required probability here.