Question

In: Statistics and Probability

A study on aggressive driving found that 45 % of drivers say that they have yelled...

A study on aggressive driving found that 45 % of drivers say that they have yelled at another driver. A random sample of 280 drivers in Halifax is selected and are asked whether they have yelled at other drivers.

1. What is the distribution of the number of sampled drivers who will say ”yes”, they have yelled at another driver? State only the name of the distribution.

2. What are the mean and standard deviation of the number of sampled drivers who will say "yes"?

The mean:

The standard deviation (Round to three decimals):

3. What is the probability that at least 135 drivers will say ”yes”, they have yelled at another driver? [Hint: use normal approximation]

4. What is the probability that at most 131 drivers will say ”yes”, they have yelled at another driver? [Hint: use normal approximation]

5. Use the normal approximation to calculate the probability that there will be exactly 131 sampled drivers who will say yes. [Hint: use normal approximation]

Expert Solution

Note : Allowed to solve 4 sub parts in one question

1. 1. What is the distribution of the number of sampled drivers who will say ”yes”, they have yelled at another driver? State only the name of the distribution.

It is binominal distribuiton since there are only two choices yes or no.Each trail is independent of the other.

2.2. What are the mean and standard deviation of the number of sampled drivers who will say "yes"?

3. What is the probability that at least 135 drivers will say ”yes”, they have yelled at another driver? [Hint: use normal approximation]

At least 135 drivers means 135 or more, hence we need to find P(X>=135) = P(X>134)

4. What is the probability that at most 131 drivers will say ”yes”, they have yelled at another driver? [Hint: use normal approximation]

At the most 131 drivers means P(X<=131) = P(X<132)

orchestra answered 2 years ago

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