The weight of a product is measured in pounds. A sample of 50 units is taken from a recent production. The sample yielded ¯y= 75 lb, and we know that LaTeX: \sigmaσ2= 100 lb. Calculate a 90 percent confidence interval for LaTeX: \text{μ}

90 percent confidence interval = [72.674 ,77.326]

Step-by-step explanation:

We are given that weight of a product is measured in pounds.

A random sample of 50 units is taken from a recent production. The sample yielded y bar = 75 lb, and we know that = 100 lb.

The Pivotal quantity for 9% confidence interval is given by;

               ~ N(0,1)

where, Y bar = sample mean = 75

                 = population standard deviation = 10

                 n = sample size = 50

So, 90% confidence interval for population mean,  is given by;

P(-1.6449 < N(0,1) < 1.6449) = 0.90

P(-1.6449 < < 1.6449) = 0.90

P(-1.6449 * < < 1.6449 * ) = 0.90

P(Y bar - 1.6449 * < < Y bar + 1.6449 * ) = 0.90

90% confidence interval for = [ Y bar - 1.6449 * , Y bar + 1.6449 * ]

                                              = [ 75 - 1.6449 * , 75 + 1.6449 * ]

                                              = [ 72.674 , 77.326 ]

Therefore, 90% confidence interval for population mean is [72.674 ,77.326] .

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step-by-step explanation:

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step-by-step explanation:

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