3. Results from a survey of urban traffic are summarized in the table below show

Question

3. Results from a survey of urban traffic are summarized in the table below showing the number of cars
allocated to each of four categories of average speed.

In a subsequent survey the speeds of 24 independent cars were measured. Among those 24 cars:
a) What is the expected number of cars that would be allocated to an average speed less than 30 mph?
b) What is the probability that exactly 15 cars would be allocated to an average speed less than 30
mph?
c) What is the probability that at least 7 cars would be allocated to an average speed less than 30
mph

Average speed (mph) 20 30 40 50 Number of Cars 86 123 168 56

Explanation / Answer

a)

Expected number = 24 * 0.48267898 = 11.58 = 12 approx

b)

Here, we would use binomial probability

n=24, x=15, p=0.48267898, q=0.5173

n!/x!(n-x)!*p^x*q^n-x

0.0624=Ans

c)

Here, we would use binomial probability

n=24, x=7 or above, p=0.48267898, q=0.5173

n!/x!(n-x)!*p^x*q^n-x

0.9826=Ans

Avg speed (mph) Number of cars Cumulative % 20 86 86 0.19861432 30 123 209 0.48267898 40 168 377 0.87066975 50 56 433 1

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