# The Dow Jones Industrial Avera

The Dow Jones Industrial Average has had a mean gain of 432 pearyear with a standard deviation of 722. A random sample of 40 yearsis selected. What is the probability that the mean gain for thesample was between 250 and 500?

0.669

0.137

0.331

0.863

Solution :

Given that,

mean = = 432

standard deviation = = 722

n = 40

= 432

=  (/$\sqrt$n)= ( 722 / $\sqrt$40 ) = 114.1582

P ( 250 < x < 500 )

P ( 250 – 432 / 114.1582 ) < ( –  / ) < ( 500 – 432 / 114.1582 )

P ( – 182 / 114.1582 < z < 68 / 114.1582 )

P ( -1.594 < z < 0.596 )

P ( z < 0.596 ) – P ( z < -1.594 )

Using z table

= 0.7244 – 0.0555

= 0.6689

Probability = 0.669

Option 0.669 is correct.

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