# Solved Assignments in Statistics / Probability Distribution category

According to the National Traffic Safety Council of Namibia, the probability that a traffic fatality will involve an intoxicated or alcohol-impaired driver is 40%. If eight traffic fatalities observed last month. a. Find the probability that the number of an intoxicated or alcohol-impaired driver is exactly three. b. Find the expected value and standard deviation of the number of intoxicated or alcohol-impaired drivers.
The lengths of paper clips produced by a factory are normally distributed with a mean of 2.52 cm and a standard deviation of 0.08 cm. (a) What is the probability that a paper clip selected at random will have a length more than 2.55 cm? (b) If 3% of the paper clips produced had a length of more than k cm, find the value of k.
The phone lines to an airline reservation system are occupied 50% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline. (a) What is the probability that for exactly three calls the lines are occupied? (b) What is the probability that for at least one call the lines are not occupied? (c) What is the expected number of calls in which the lines are all occupied?
A town recently dismissed 7 employees in order to meet their new budget reductions. The town had 8 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that no employees were over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.
The computer that controls a bank's automatic teller machine crashes a mean of 0.4 times per day. What is the probability that, in any seven-day week, the computer will crash less than 2 times? Round your answer to four decimal places.
A well-mixed cookie dough will produce cookies with a mean of 8 chocolate chips apiece. What is the probability of getting a cookie with at least 4 chips?
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 4. Calculate the probability of getting no more than 5 calls between eight and nine in the morning. Round your answer to four decimal places.
Unknown to a medical researcher, 10 out of 17 patients have a heart problem that will result in death if they receive the test drug. 6 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that less than 5 patients will die? Express your answer as a fraction or a decimal number rounded to four decimal places.
A company produces optical-fiber cable with a mean of 0.7 flaws per 100 feet. What is the probability that there will be exactly 3 flaws in 1100 feet of cable? Round your answer to four decimal places.
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 30% of this population prefers the color brown. If 12 buyers are randomly selected, what is the probability that exactly 5 buyers would prefer brown? Round your answer to four decimal places.