Question

Sampling Distribution

1. A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the
expenditure is $3. A simple random sample of 64 students is taken.

A. What is the expected value, standard deviation, and shape of the sampling distribution of the
sample mean?
B. What is the probability that these 64 students will spend a combined total of more than
$715.21?
C. What is the probability that these 64 students will spend a combined total between $703.59 and
$728.45?

Answer 1

The solution to this problem is given by

Solution amount spends in S. Led hou. 'x' denote the &(x) = M = 100 50 3 of Y= {xi denote total of na 64 students, then distribution is approximate normal mean Standald deviation or its eqe, and with when 13 que nu 10.50 X64 = 672 unod √64x32 3x8 =24 Exin Nl 678,24%) (B) Pl total of more than 715.21) EPL Y 3715:21) =pl 715.21~672 24 - Play 1. 800 0.035897 = 0.0359 Youn ㄷ 0·0359

(C) Probability that total between 703.59 and 798.45 그 PL = 703.59 Lexi <728.45) P( 703.59 <Y C 798.45) You, 272845-672 24 31625 LZL 2.35208) Pl 0.084711 - 010847