Question

# The mean of a normal probability distribution is 390; the standard deviation is 14. a. About...

The mean of a normal probability distribution is 390; the standard deviation is 14.

a. About 68% of the observations lie between what two values?

Lower Value

Upper Value

b. About 95% of the observations lie between what two values?

Lower Value

Upper Value

c. Nearly all of the observations lie between what two values?

Lower Value

Upper Value

Solution :

Given that,

= 390

= 14

Using Empirical rule,

(a)

P( - 1< X < + 1) = 68%

P ( 390 - 1* 14 < X < 390 + 1* 10) = 68%

P ( 376 < X < 404 ) = 68 %

Lower Value = 376

Upper Value = 404

(b)

P( - 2< X < + 2) = 95%

P ( 390 - 2 * 14 < x < 390+2 *14 ) = 95 %

P( 362 < x < 418 ) = 95 %

Lower Value = 362

Upper Value = 418

(c)

P( - 3< X < + 3) = 99.7%

P( 390 - 3 *14 < X < 390+ 3* 14 ) = 99.7%

P( 348 < X < 432 )= 99.7%

Lower Value = 348

Upper Value = 432

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