Question

For questions 1-4 use the following scenario

A specific study found the average of doctor visits per year for people over 55 is 8 with a standard deviation of 2. Assume that the variable is normally distributed.

1. Identify the population mean

2. Identify the population standard deviation

3. Suppose a random sample of 15 people over 55 is selected. What is the probability that the sample mean is above 9?

4. Suppose a random sample of 10 people over 55 is selected. What is the probability that the sample mean will be below 7?

For questions 5-8 use the following scenario

A study found that citizens spend on average $1950 per year on groceries with a standard deviation of $400. Assume that the variable is normally distributed.

5. Identify the population mean

6. Identify the population standard deviation

7. Find the probability that a sample of 20 citizens will have a mean less than $1800

8. Find the probability that a sample of 50 citizens will have a mean less than $2000

Answer 1

Solution:-

1) The population mean is 8.

2) The population standard deviation is 2.

3) The probability that the sample mean is above 9 is 0.026.

n = 15

x = 9

By applying normal distribution:-

$z = \frac{x-\mu }{\frac{\sigma }{\sqrt{n}}}$

z = 1.94

P(z > 1.94) = 0.026.

4) The probability that the sample mean will be below 7 is 0.057.

n = 10

x = 7

By applying normal distribution:-

$z = \frac{x-\mu }{\frac{\sigma }{\sqrt{n}}}$

z = -1.581

P(z < - 1.581) = 0.057