1. A radar unit is used to measure the speed of automobiles on the expressway during the rush-hour traffic. The speed of individual automobiles are normally distributed with a mean of 62 mph. (a) If the standard deviation is about 4.95 mph, what is the proportion of the cars that are traveling in 70 mph or less? (b) Find the 25th percentile, using the standard deviation of Part (a). (c) If 3% of the automobiles travel faster than 72 mph, what is the standard deviation? (d) Find the proportion of the cars that are traveling faster than 55 mph, using the standard deviation found in Part (c). (e) Find the 95th percentile, using the standard deviation of Part (c).

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.