hwk&rec5

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308

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Statistics

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Apr 3, 2024

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Uploaded by ChancellorBravery101240

STAT 308 Homework #5 Due Tuesday March 19 Spring 2024 NOTE: All questions should be handed in. Selected questions would be graded. *** USE EXCEL ONLY TO ANSWER THE LAST QUESTION OF ASSIGNMENT *** *** FOR ALL OTHERS USE TABLES AND SHOW WORK. NO WORK NO CREDIT *** 1. Find the area under the standard normal curve that lies a. to the right of -1.07 b. to the right of 4.2 c. to the left of 4.2 d. between -2.18 and 1.44 e. between 1.1 and 4.2 f. either to the left of -2.12 or to the right of 1.67 g. either to the left of 0.63 or to the right of 1.54 2. Obtain the following z-scores. (Choose the closest value. If halfway, then interpolate). a. z 0.20 b. z 0.005 3. An article by S. M. Berry titled “Drive for Show and Putt for Dough ( Chance , Vol 12(4), pg 50-54) ” discussed the driving distances of PGA players. The mean distance for tee shots on the 1999 men ’s PGA tour is 272.2 yards with a standard deviation of 8.12 yards. Assuming that the 1999 tee-shot distances are normally distributed, find the percentage of such tee shots that went a. between 260 and 280 yards. b. more than 300 yards. 4. Do Exercise 6.103 on page 288 in the textbook. Show work. 5. Refer to question 3 in this homework. The article “Drive for Show and Putt for Dough ( Chance , Vol 12(4), pg 50-54) ” discussed driving distances of PGA players. The mean distance for tee shots on the 1999 men ’s PGA tour is 272.2 yards with a standard deviation of 8.12 yards. Assuming that the 1999 tee-shot distances are normally distributed answer the following questions: a. Determine the quartiles of the driving distances b. Find the 95 th percentile. c. Obtain the third decile (i.e. 30 th percentile). d. Interpret your answers in parts a-c 6. Use Excel to answer questions (3), (4) and (5) a-c above. Label questions appropriately in Excel worksheets. Hand in Excel output. -1-

Exercises for recitations 1. Using the standard normal probability table find the area that a. lies to the right of -1.37 b. lies to the left of 1.42 c. lies between -1.35 and 0.19 d. lies either to the left of -2.5 or to the right of 1.78. 2. Complete the following table (read the closest value from the Normal table) z 0.10 z 0.05 z 0.025 z 0.01 1.645 1.96 3. As reported by the US National Center for Health Statistics, males who are 6 ft tall and between 18 and 24 years of age have a mean weight of 175 lb. If the weights are normally distributed with a standard deviation of 14 lb, find the percentage of such males that weigh a. between 190 and 210 lb. c. at least 160 lb. b. less than 150 lb. d. at least 190 lb. th e. find the 90 percentile of the distribution of weight of males who are 6 ft tall and between 18 and 24 years of age. (Use the closest value from Normal table) 4. Repeat exercises (1) to (3) using Excel. Excel Instructions The following functions applied to both, PCs and MACs. Working with the Standard Normal Distribution : NORMSDIST(z) returns the probability that the observed value of a standard normal random variable will be less than or equal to z. That is, returns the area to the left of the given z-cores Syntax =NORMSDIST(z) where z is a z-score. NORMSINV(probability) returns the inverse of the standard normal cumulative distribution. That is, returns the z-scores with an area to the left equal to the probability Syntax =NORMSINV(probability) where probability is a probability corresponding to the normal distribution. Working with ANY Normal Distribution : -2-

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