In a large city, 65% of people pass the drivers\' road test. Suppose that every

Question

In a large city, 65% of people pass the drivers' road test. Suppose that every day 400 people independently take the test. Complete parts (a) through (d) below a. What is the number of people who are expected to pass? (Round to the nearest whole number as needed.) b. What is the standard deviation for the number expected to pass? The standard deviation is (Round to the nearest whole number as needed.) C. After a great many days, according to the Empirical Rule, on about 95% of these days, the number of people passing will be as low as and as high as (Hint: Find two standard deviations below and two standard deviations above the mean.) After a great many days, according to the Empirical Rule on about 95% of these days, the number of people passing will be as low as (Round to the nearest whole number as needed.) d. If you found that one day, 315 out of 400 passed the test, would you consider this to be a very high number? and as high as V because 315 is V above the mean less than 1 standard deviation between 1 and 2 standard deviations between 2 and 3 standard deviations more than 3 standard deviations

Explanation / Answer

a) Expected number = n * p = 400 * 0.65 = 260

b) standard deviation = sqrt(n * p * (1 - p))

                                    = sqrt(400 * 0.65 * 0.35) = 10

c) Low value = 260 - 2 * 10 = 240

High value = 260 + 2 * 10 = 280

The no of passing will be as low as 240 and as high as 280

d) Yes because 315 is more than 3 standard deviation above the mean.

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