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1. The heights of boys at a particular age follows a normal distribution with mean 150.3 cm and standard deviation 5 cm. Find the probability that a boy picked at random from this age group has height
(a) less than 153 cm
(b) less than 148 cm
(c) more than 158cm
(d) more than 144 cm
(e) between 147 cm and 149.5cm
(f) between 150 cm and 158 cm
2. The mean mark on a final examination was 72 and the standard deviation was 9. The top 10% of the students are to receive A’s. What is the minimum mark a student must get in order to receive an A ?
3. In a manufacturing process, the time spend in the assembly line may be looked upon as a random variable having a normal distribution with a mean of 13.2 mins and a standard deviation of 0.10 mins.
(a) Find the probability that it will take at least 13.0 mins to assemble one of the process. (b) What is the length of time above which will be the slowest 10% of the assembly time ?
4. If X~N(100,36) and P(X>a) = 0.1093, find the value of a.
5. Each weekday Mr Jones walks to the local library to read the newspapers. The time he takes to walk to and from the library is a normal variable with mean 15 minutes and standard deviation 2 minutes. The time he spends in the library is a normal variable with mean 25 minutes and standard deviation minutes. Find the probability that, on a particular day (a) Mr. Jones is away from the house for more than 45 minutes. (b) Mr. Jones spends more time traveling than in the library.
6. It is estimated that of the population of England watched last year’s Cup Final on television. If random samples of 100 people are interviewed,
(a) calculate the mean and variance of the number of people from these samples who watched the Cup Final on television.
(b) calculate the probability that more than 30 people watched the Cup Final on television.
7. Four hundred pupils sit a test which consists of 80 true-false questions. None of the candidates knows any of the answers and so guesses.
(a) If the
(a) less than 153 cm
(b) less than 148 cm
(c) more than 158cm
(d) more than 144 cm
(e) between 147 cm and 149.5cm
(f) between 150 cm and 158 cm
2. The mean mark on a final examination was 72 and the standard deviation was 9. The top 10% of the students are to receive A’s. What is the minimum mark a student must get in order to receive an A ?
3. In a manufacturing process, the time spend in the assembly line may be looked upon as a random variable having a normal distribution with a mean of 13.2 mins and a standard deviation of 0.10 mins.
(a) Find the probability that it will take at least 13.0 mins to assemble one of the process. (b) What is the length of time above which will be the slowest 10% of the assembly time ?
4. If X~N(100,36) and P(X>a) = 0.1093, find the value of a.
5. Each weekday Mr Jones walks to the local library to read the newspapers. The time he takes to walk to and from the library is a normal variable with mean 15 minutes and standard deviation 2 minutes. The time he spends in the library is a normal variable with mean 25 minutes and standard deviation minutes. Find the probability that, on a particular day (a) Mr. Jones is away from the house for more than 45 minutes. (b) Mr. Jones spends more time traveling than in the library.
6. It is estimated that of the population of England watched last year’s Cup Final on television. If random samples of 100 people are interviewed,
(a) calculate the mean and variance of the number of people from these samples who watched the Cup Final on television.
(b) calculate the probability that more than 30 people watched the Cup Final on television.
7. Four hundred pupils sit a test which consists of 80 true-false questions. None of the candidates knows any of the answers and so guesses.
(a) If the