Normal distribution assignment
- 1. Applied 40S Normal Distribution Assignment 1. Find the z-score in a normal distribution that cuts off: a. the top 30% b. the top 68% c. the bottom 20% d. the bottom 65% 2. Find the z-score if the area under a standard normal curve: a. to the right of z is 0.188 b. to the left of z is 0.695 c. to the left of z is 0.215 3. Find the percent of z-scores in a normal distribution (non-standard) with = 75 and = 10 that are between: a. 70 and 80 b. greater than 71 c. less than 69 4. Determine the values for z and x. 5. A college aptitude test is scaled so that its scores approximate a normal distribution with a mean of 500 and standard deviation of 100. a. Find the probability that a student selected at random will score 800 or more points. b. Find the score x, such that 76 percent of the students have a score less than x. 6. The lifetimes of a certain kind of light bulb are approximately normally distributed with a mean of 950 hours and a standard deviation of 60 hours. a. Find the probability that a bulb will last less than 1000 hours. b. Find the time, T, such that the probability that a bulb will last more than T is 0.92.
- 2. 7. The weights of babies born in a certain hospital average 8 lb 1 oz, with a standard deviation of 12 oz. Assume that the weights are normally distributed. Be sure to convert oz. to lbs, 1lb=16oz.. a. Find the percentage of babies with a birth weight between 7 and 9 pounds. b. Find the weight, W, such that the percentage of babies with a birth weight greater than W is 60 percent. c. Find the weight, W, such that the percentage of babies with a birth weight less than W is 25 percent. 8. A teacher finds that the results on a final exam are normally distributed with a mean of 62 percent and a standard deviation of 12. a. If the passing grade is 52 percent, what percent of the class will fail? b. If the teacher wants only 75 percent of the class to pass, what should the passing mark be? c. If the teacher wants only 8 percent of the class to get an A, what grade must a student have to get an A? Answers: 1. a) 0.524 2. a) 0.885 3. a) 38.3% b) -0.468 b) 0.510 b) 65.5% c) –0.842 c) –0.789 c) 27.4% d) 0.385 4. z= -0.524, x= 151.3 5. a) 0.001 or 0.1% 6. a) 0.798 b) 570.6 b) 865.7 hours 7. a) 81.6% 8. a) 20.2% b) 126 oz or 7.87 lbs or 7lbs 14 oz b) 54% c) 7 lb 9 oz c) 79%