Question

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 92 hours. A random sample of 64 light bulbs indicated a sample mean life of 360 hours. Complete parts (a) through (d) below. that the lightbulbs have a mean life of 410 hours. c. Must you assume that the population light bulb life is normally distributed? Explain. O A. Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. O B. Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. O C. No, since o is known and the sample size is large enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem. OD. No, since o is known, the sampling distribution of the mean does not need to be approximately normally distributed. d. Suppose the standard deviation changes to 76 hours. What are your answers in (a) and (b)? The 99% confidence interval estimate would be from a lower limit of (Round to one decimal place as needed.) hours to an upper limit of hours. the right to state that the lightbulbs have a mean life of 410 hours. A mean of 410 hours is standard errors Based on the sample data and a standard deviation of 76 hours, the manufacturer the sample mean, so it is that the lightbulbs have a mean life of 410 hours.

Answer 1

Solution-

• 99% confidence interval at standard deviation = 92
• (330.4 , 389.6)

Sample Mean X = 360 Population Standard Deviation (0) = 92 Sample Size (N) = 64 The critical value for a = 0.01 is Zc = 21-a/2 = 2.576. The corresponding confidence interval is computed as shown below: ci = (x – mex Tom.X + ze x porn) = (360 – 2.576 om, 360 + 2.576 %*) = (330.378, 389.622) Therefore, based on the data provided, the 99% confidence interval for the population mean is 330.378 < u < 389.622, which indicates that we are 99% confident that the true population mean u is contained by the interval (330.378, 389.622).

C)

Option c is correct.

c. No, since sigma is known and the sample size is large enough, the sampling distribution of mean is approximately normal by central limit theorem.

d)

99% confidence interest of mean when standard deviation = 76.

The 99% confidence interview esto mate will be From a lower limit of 335.5 hours to an upper limit of 384.5 hours.

We need to construct the 99% confidence interval for the population mean . The following information is provided: Sample Mean X = 360 Population Standard Deviation (0) = 76 Sample Size (N) = 64 The critical value for a = 0.01 is ze = 21-a/2 = 2.576. The corresponding confidence interval is computed as shown below: CI = (x-zex Porns + ze x porn) = (360 – 2.576 762360 + 2.576 76) (335.53, 384.47) Therefore, based on the data provided, the 99% confidence interval for the population mean is 335.53 < < 384.47, which indicates that we are 99% confident that the true population mean u is contained by the interval (335.53, 384.47).