Question

8. A random variable is normally distributed with a mean of μ=50 and a standard deviation of σ = 5.

   1. a) Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45, 50, 55, 60, and 65.

   2. b) What is the probability the random variable will assume a value between 45 and 55?

   3. c) What is the probability the random variable will assume a value between 40 and 60?

   4. d) Draw a graph for the standard normal distribution. Label the horizontal axis at values of -3, -2, -1, 0, l, 2, and 3.

Answer 1

Given:

= 50, = 5

a)

b)

68.27% of the values of x are within

Therefore,

P(45 X 55) = 0.6827

C)

95.45% of the values of x are within  

Therefore,

P(40 X 60) = 0.9545

d)

In Standard Normal distribution:

= 0 and = 1