Question

From a normally distributed population, a simple random sample of size 30 is taken. The mean of the sample is 144 and the standard deviation of the sample is 12.

Which interval is the 90% confidence interval for the population mean?

(142.4, 145.6)

(143.3, 144.7)

(140.4, 147.6)

(139.7, 148.3)

Answer 1

90% confidence interval for the population mean is  140.4  & 147.6

Step-by-step explanation:

Mean  = 144

SD = 12

n = Sample size = 30

90% confidence interval

= 0.9

1 - 0.9 = 0.1

0.1/2 = 0.05

Z score for 1 -0.05 = 0.95  is  1.645

144  ± Z * SD/√n

= 144 ±  (1.645) 12/√30

= 144 ±  3.6

= 140.4  & 147.6

90% confidence interval for the population mean is  140.4  & 147.6

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