Is lack of sleep causing traffic fatalities? A study conducted under the auspice

Question

Is lack of sleep causing traffic fatalities? A study conducted under the auspices of the National Highway Traffic Safety Administration found that the average number of fatal crashes caused by drowsy drivers each year was 1500. Assume the annual number of fatal crashes per year is normally distributed with a standard deviations of 300. What is the probability of fewer than 1000 fatal crashes in a year? What is the probability the number of fatal crashes will be between 1000 and 2000 for a year? For a year to be in the upper 5% with respect to the number of fatal crashes, how many crashes would have to occur?

Explanation / Answer

C) For a 95% confidence level the value of Z from the normal distribution table = 1.96

Z = (X - Mean ) / Standard deviation

Z = ( X - 1500 ) / 300

1.96 = X - 1500 / 300

X = 2088

The number of crashes would have to occur = 2088 .

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