Invert Norm Questions

  1. The life of a bread machine is found to be normally distributed with a mean life of 5.2 years and a standard deviation of 0.8 years. The producer of the bread machines will replace broken bread machines free of charge while under warranty. For how many years should the producer guarantee the toasters if no more than 5% of them are to be replaced? Justify your answer.
  1. Scores on a certain college entrance test are normally distributed with a mean of 325. If the probability of a score being greater than 350 is 2.5%, what is the standard deviation of the distribution?
  1. Scores on a scholarship exam are normally distributed with a standard deviation of 25. If the probability of a score being less than or equal to 188 is 0.61 determine the mean of them scores on this scholarship exam, to the nearest whole number.
  1. Mr. Bennet writes his exam in hopes that 95% of all students will pass. If the average mark on the exam is 65%, with a standard deviation of 8%, what should the passing grade be?
  1. The brake lining thickness for a number of vehicles is recorded and found to be distributed normally. The mean thickness is 12.7 mm with a standard deviation of 2.1 mm.

a)Calculate the probability that a vehicle selected at random will have a brake lining thickness from 10.5 mm to 11.5 mm (inclusive).

b)What is the z-score associated with a brake lining thickness of 12.0 m

c)The mechanic tells you that only 25% of all cars have brake linings thinner than those on your family car. How thick are the brake linings on your car? Support your answer.

  1. The height of adult females in Canada is normally distributed with a mean of 164 cm and a standard deviation of 4.10 cm.

a)Prior to 1985, the Winnipeg Police Service considered a height of 157 cm or less to be too short for women to join the police service. What percentage of adult females would have been too short to join the police force at that time? Indicate your strategy.

b)At that time, approximately 11.10% of adult females were too short to enlist in the Brandon Police Service. What minimum height was being used in the Brandon Police Service selection process? Indicate your strategy.