Highway engineers have found that the ability to see and read a sign at night depends in part on its “surround luminance.” That is, it depends on the light intensity near the sign. These data are obtained on the surround luminance (in candela per square meter) of 30 randomly selected highway signs in a large metropolitan area. (Based on “Use of Retroreflectors in the Improvement of Nighttime Highway Visibility,” H. Waltman, Color  , 1990, pp. 247−251.):

a. Find the sample variance for these data. 

b. Assume that the data are drawn from a normal distribution. Find a 90% confidence interval on the variance in the surround luminance in this area. 

c. Find a 90% confidence interval on the standard deviation in surround luminance. 

d. The normal probability rule (Sec. 4.5) implies that a normal random variable will lie within two standard deviations of its mean with probability .95. Use X and S to estimate the mean and standard deviation of the surround luminance in this area. Would it be unusual for the surround luminance for a randomly selected sign to exceed 18 cd/m ²  ? Explain.