Question

Listed below are the amounts of net worth​ (in millions of​ dollars) of the ten wealthiest celebrities in a country. Construct a

99​%

confidence interval. What does the result tell us about the population of all​ celebrities? Do the data appear to be from a normally distributed population as​ required?

262

200

199

158

157

151

145

145

145

140

What is the confidence interval estimate of the population mean μ​?

___ million less than<mu μless than<​____million

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 170.2

S = 38.94954001

n = 10

df = n – 1 = 9

Confidence level = 99%

Critical t value = 3.2498

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 170.2 ± 3.2498*38.94954001/sqrt(10)

Confidence interval = 170.2 ± 40.0280

Lower limit = 170.2 - 40.0280 = 130.17

Upper limit = 170.2 + 40.0280 = 210.23

130.17 million < µ < 210.23 million