Question

In a large​ city, 6060​% of people pass the​ drivers' road test. suppose that every​ day, 300300 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 180180. ​(round to the nearest whole number as​ needed.)
b. what is the standard deviation for the number expected to​ pass? the standard deviation is nothing. ​(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 nothing and as high as nothing. ​(round to the nearest whole number as​ needed.)
d. if you found that one​ day, 134134 out of 300300 passed the​ test, would you consider this to be a very lowlow ​number? ▼ yes, no, because 134134 is ▼ less than 1 standard deviation between 1 and 2 standard deviations between 2 and 3 standard deviations more than 3 standard deviations belowbelow the mean.

Answer 1

A) 180 would be expected to pass.
B) The standard deviation is 4.
C) 95% of people would fall between 172 and 188.
D) Yes, this is more than 3 standard deviations below the mean.

Explanation
A) Multiply the probability by the sample size:
0.6(300) = 180

B) Standard deviation is found by:
√n(p)(1-p)
For our data, we have:
√300(0.6)(0.4) = 4

C) Two standard deviations below the mean is 180-2(4) = 172; two standard deviations above the mean is 180+2(4)= 188.

D) Three standard deviations below the mean is 180-3(4) = 168; 134 is more than this below the mean.  99.7% of data fall within 3 standard deviations of the mean; 0.15% fall below this point, so yes, this is unusually low.