Question

) For 30 randomly selected Rolling Stones concerts, the mean gross earnings is 2.79 million dollars. Assuming a population standard deviation gross earnings of 0.47 million dollars, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions). g

Answer 1

Answer:

the confidence interval is from 2.6 million to 3.01 million

Step-by-step explanation:

Using this formula X ± Z (s/√n)

Where

X = 2.79 million = 2790000 --------------------------Mean

S = 0.47 million = 470000 ----------------------------- Standard Deviation

n = 30 ----------------------------------Number of observation

Z = 2.576 ------------------------------The chosen Z-value from the confidence table below

Confidence Interval Z

80%. 1.282

85% 1.440

90%. 1.645

95%. 1.960

99%. 2.576

99.5%. 2.807

99.9%. 3.291

Substituting these values in the formula

Confidence Interval (CI) = 2790000 ± 2.576 (470000 / √30)

CI = 2790000 ± 2.576 (470000 / 5.477)

CI = 2790000 ± 2.576 (85813.4015)

CI = 2790000 ± 221,055.3223

CI = 2790000 + 221,055.3223 ~. 2790000 - 221,055.3223

CI = 3,011,055.3223 ~ 2,568,944.6777

CI = 3.01 million. ~ 2.6 million (Approximated)

In other words the confidence interval is from 2.6 million to 3.01 million