In a large city, 6060% of people pass the drivers' road test. suppose that every day, 300300 people independently take the t
est. 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.
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.
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