Question

The Dow Jones Industrial Average has had a mean gain of 432 pear year with a standard deviation of 722. A random sample of 40 years is selected. What is the probability that the mean gain for the sample was between 200 and 500?

0.703

0.297

0.836

0.164

Answer 1

n = 40, = 432, = 722

Z = (X – )/[/Sqrt(n)]

To calculate P (200 < X < 500) = P(X < 500) – P(X < 200)

For P( X < 500)

Z = (500 – 432)/[722/Sqrt(40)] = 0.596

The probability for P(X < 500) from the normal distribution tables is = 0.7243

For P( X < 200)

Z = (200 – 432)/[722/Sqrt(40)] = -2.032

The probability for P(X < 200) from the normal distribution tables is = 0.02106

Therefore the required probability is 0.7243 – 0.02106 = 0.70324     0.703