Classwork: Normal Distribution Complete the following questions in each section. **Draw a picture for each problem** Find the area under the standard normal distribution for each: 1) Between z = 1.10 and z = -1.80 2) To the right of z = 1.75 3) To the left of z = 1.36 4) Between z = -1.20 and z = -2.25 Use the formula given to find the probabilities for each: z = 5) On the daily run of an express bus, the average number of passengers is 48. The standard deviation is 3. Assume the variable is normally distributed. Find the probability that the bus will have a. Between 36 and 40 passengers b. Less than 42 passengers 6) The length of time required to assemble a photoelectric cell is normally distributed with a mean of 18.1 minutes and standard deviation is 1.3 minutes. What is the probability that it will require more than 20 minutes to assemble a cell? Use the formula given: X = z (σ) + µ 7) Membership in an elite organization requires a test score in the upper 30% range. If the mean is 115 and standard deviation is 12, find the lowest acceptable score that would enable a candidate to apply for membership. Assume the variable is normally distributed. 8) A physical fitness association is including the mile run in their secondary school fitness test for boys. The time for this event for boys in secondary schools is approximately normally distributed with a mean of 450 seconds and a standard deviation of 40 seconds. If the association wants to designate the fastest 10% as “excellent,” what time should the association set for this criterion? (faster people have lower times) Use the formula given to find the probability: z= 9) The average repair cost of a microwave oven is $55. The costs are normally distributed and have a standard deviation of $8. If 12 ovens are repaired, find the probability that the mean of the repair bills will be greater than $60? 10) The mean grade point average of the engineering majors at a large university is 3.23, with a standard deviation of 0.72. In a class of 48 students, find the probability that the mean grade point average of the students is less than 3.15.
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