In a large city, 55% of people pass thedrivers' 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? The expected number is 220. (Round to the nearest whole number asneeded.) b. What is the standard deviation for the number expected to pass? The standard deviation is 10. (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 _and as high as ___.(Round to the nearest whole number as needed

c) After a great many days, regarding the Empirical Rule, on about 95% of these days, the number of people passing will be as low as 200 and as high as 240.

Step-by-step explanation:

a) The number of people expected to pass = np = 400*0.55 = 220

b) Standard deviation = \sqrt{npq} = \sqrt{400*0.55*0.45} = 10

c) Regarding the empirical rule, 95% of the observations lie within 2 SD from the mean. Therefore,

Lower bound = 220 - 2*!0 = 200

Upper bound = 220 + 2*10= 240

After a great many days, regarding the Empirical Rule, on about 95% of these days, the number of people passing will be as low as 200 and as high as 240.

ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2025-03-26T03:37:05-04:00

After a great many days, regarding the Empirical Rule, on about 95% of these days, the number of people passing will be as low as 200 and as high as 240.

It is given that

55 % of people pass the drivers' road test and 400 people independently take the test.

So, the number of people who are expected to pass = 400*0.55 = 220

What is the standard deviation formula for binomial distribution?

Standard deviation is the square root of variance i.e [tex]\sqrt{npq}[/tex]

Where n is no of trials while p and q are complementary probabilities.

Standard deviation =[tex]\sqrt{400*0.55*0.45}[/tex] = [tex]\sqrt{99}[/tex] =9.95≈10

Two standard deviation below the mean = 220-2*10 =200

Two standard deviation above the mean= 220 + 2*10= 240

Therefore, After a great many days, regarding the Empirical Rule, on about 95% of these days, the number of people passing will be as low as 200 and as high as 240.

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