Question

Use the confidence level and sample data to find a confidence interval for estimating the population muμ. Round your answer to the same number of decimal places as the sample mean. A random sample of 9595 light bulbs had a mean life of x overbar equals 510x=510 hours with a standard deviation of sigma equals 37 hours.σ=37 hours. Construct a​ 90% confidence interval for the mean​ life, muμ​, of all light bulbs of this type.

Answer 1

Answer:= (504, 516)

Therefore, the 90% confidence interval (a,b) = ( 504, 516)

Explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean gain x = 510

Standard deviation r = 37

Number of samples n = 95

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

510+/-1.645(37/√95)

510+/-1.645(3.796)

510+/-6.24

510+/-6

= (504, 516)

Therefore at 90% confidence interval (a,b) = ( 504, 516)