Question

In an orthopedic office, the patients ages roughly follow a normal distribution with a mean age of 62 years old and a standard deviation of 4.6 years. What is the probability that a patients age is more than 56 years old?

Group of answer choices

0.0968

0.9

0.9032

0.9049

Answer 1

In an orthopedic office, the patient's ages roughly follow a normal distribution with a mean age of 62 years, and a standard deviation of 4.6 years.

So, if X is the random variable denoting the age of a randomly selected patient, then X follows normal distributon with mean 62 and standard deviation of 4.6 years.

So, we can say that Z=(X-62)/4.6 follows standard normal distribution with mean 0 and standard deviation 1.

Now, we have to find the probability that a patient's age is more than 56 years.

So, we have to find

Where, phi is the distribution function of the standard normal variate.

So, the required answer is option (c) 0.9032.