Question

A set of exam scores is normally distributed with a mean = 82 and standard deviation = 4. Use the Empirical Rule to complete the following sentences. 68% of the scores are between and . 95% of the scores are between and . 99.7% of the scores are between and . LicensePoints possible: 3 This is attempt 1 of 3.

Answer 1

solution

Solution :

Given that,

= 82

= 4

Using Empirical rule,

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

P(82 - 4 < X < 82+ 4) = 68%

P(78 < X < 86) = 68%

Answer = 78 and 86

(B)

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

P(82 - 2 * 4 < X < 82 + 2 * 4) = 95%

P(74 < X < 90) = 95%

Answer =Answer = 74 and 90

(C)

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

P(82 - 3 * 4 < X < 82 + 3 * 4) = 99.7%

P(70 < X < 94) = 99.7%

Answer =Answer = 70 and 94