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For drivers aged 20-24 there is a 34% chance of having a car accident in a...

For drivers aged 20-24 there is a 34% chance of having a car accident in a one year period (based on data from the National Safety Council).
(a) Based on this data, in a group of 11 randomly selected drivers aged 20-24, find the probability that at least 2 of them will have a car accident in the next year.
(b) In a group of 260 drivers aged 20-24, find the mean number of drivers who will have a car accident in the next year.
(c) In a group of 260 drivers aged 20-24, find the standard deviation of the number of drivers who will have a car accident in the next year.
(d) Suppose that a group of 260 drivers aged 20-24 are randomly selected, and 106 of them have had a car accident in the last year. Is this a significantly high number that would perhaps suggest that the given percentage of drivers aged 20-24 that have a car accident in a one year period (i.e., 34%) is not correct?

Solutions

Expert Solution

The probability of having a car accident in a one year period is p = 0.34

a) n = 11

Let X be the number of drivers having a car accident ina one year period.

X ~Binomial( 11 , 0.34)

The probability that at least 2 of them will have a car accident in the next year is

b) When n = 260

Mean = np = 260*0.34 = 88.4

The mean number of drivers who will have a car accident in the next year is 88.4

c)  When n = 260

Variance ( ) = npq = 260*0.34*0.66 = 58.344

Standard deviation () =

The standard deviation of the number of drivers who will have a car accident in the next year is 7.6383

d) In a group of 260 drivers, the percentage of them had a car accident in the last year is  

= (106/260)*100 =40.77%

Mean number of accidents in the last year is

and Standard deviation is

The maximum Limit is

Yes the 106 accidents are significantly high numbers  that would perhaps suggest that the given percentage of drivers aged 20-24 that have a car accident in a one year period.

milcah answered 1 year ago
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