Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name:_________________________ Date:_____________ Chapter 6 Test : Normal Probability Distributions 1 Applied and Computational Questions 14. 15. 16. 17. 18. 19. 20. 21. 22. The random variable z is the standard normal score. Find z as shown in the diagram below given that the area of the shaded region is 0.4927. z ANSWER: _____________ 0 When using the notation z ( ) , the number in parenthesis is the measure of the area to the right of the z-score. Use this fact to find the z value corresponding to a. z(0.08) ANSWER: _________________ b. z(0.78) ANSWER: _________________ c. z(0.8980) ANSWER: _________________ d. z(0.50) ANSWER: _________________ Find the probability that a piece of data picked at random from a normal population would have a standard score, z, that lies: a. Between z = 0 to z = -1.89 ANSWER: _________________ b. To the left of 1.01 ANSWER: _________________ c. To the right of -2.35 ANSWER: _________________ d. Between z = 0.61 to z = 2.93 ANSWER: _________________ Find the probabilities: a. P(-2.10<z<2.35) ANSWER: _________________ b. P(z>0.13) ANSWER: _________________ c. P(z<3.67) ANSWER: _________________ d. P(1.28<z<2.86) ANSWER: _________________ Suppose daycare costs are normally distributed with a mean equal to $7000, and a standard deviation equal to $1500. a. What percentage of daycare centers cost between $4000 and $8000? ______ b. What percentage of daycare centers cost more than $9000? ____________ c. What percentage of daycare centers cost less than $5000? ________________ Find the z-score for the standard normal distribution such that: a. 80% of the distribution is below(to the left of) this value ____________ b. The area to the right of this value is .15 ______________________________ Find the normal approximation for the binomial probability P(x≥9), where n = 12 p = 0.75.Compare this to the value you obtain using the binomial probability function P(x≥9). Normal approximation of probability: ________________________ Binomial probability: _________________________ X has a normal distribution with a mean of 75.0 and a standard deviation of 2.5. Find the following probabilities: a. P(X < 70.0) __________________ b. P(72.5 <X < 80.0) __________________ c. P(X > 82.5) __________________ Use the standard normal table to find the following values of z: a. z(0.9940) __________________ b. z(0.2054) __________________ c. z(0.3315) __________________ d. z(0.7881) __________________ Name:_________________________ Date:_____________ Chapter 6 Test : Normal Probability Distributions 23. 24. Consider a binomial distribution with 15 identical trials, and probability of success of 0.5. a. Use the binomial tables to find P(3 < x 7). __________________ b. Use the normal approximation to find P(3 < x 7). __________________ Find the probability that a piece of data picked at random from a normally distributed population will have a standard score that is a. b. c. d. e. 25. 26. 2 less than 2.00 greater than –1.40 less than –1.75 less than 1.25 greater than –1.58 __________________ __________________ __________________ __________________ __________________ Given that x is a normally distributed random variable with a mean of 70 and a standard deviation of 10, find the following probabilities. a. P(x > 70) __________________ b. P(70 < x < 82) __________________ c. P(67 < x < 93) __________________ d. P(75 < x < 92) __________________ e. P(48 < x < 88) __________________ f. P(x < 48) __________________ The SAT scores attained by the students in Iowa City are approximately normally distributed with a mean of 500 and a standard deviation of 80. a. Find the percentage of students who score between 550 and 650. b. Find the percentage of students who score less than 700. __________________ c. Find the 3rd quartile __________________ th d. Find the 15 percentile, P15 __________________ th e. Find the 95 percentile, P95 __________________