Question

At a large university, the students have an average creditcarddebt of $2500,with a standard deviation of $1200. If we consider all of the possible random samples of 100students at this university, 95% of thesamples should have means between what two numbers? [HINT-use the 68-95-99.7Rule table in conjunction with the values for the sampling distribution model]

A)$100 and $2620

(B)$300 and $4900

(C)$2140 and $2860

(D)$2260 and $2740

Answer 1

Solution :

Given that,

= 2500

= 1200

= 100 and

= / n = 1200 / 100 = 1200 / 10 = 120

Using Empirical rule,

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

P(2500 - 2 * 120 < X < 2500 * 2 * 120) = 95%

P(2260 < X < 2740) = 95%

D) $2260 and $2740