Entry to a certain University is determined by a national test, The scores on this test are no distributed with a mean of 492 and a standard deviation of 87. Use this information to ansy questions 12-18. 12) Based on the empirical rule, 68% of the data will fall within what interval? (405. 579 ) 13) Based on the empirical rule, 95% of the data will fall within what interval? (318 606) 14) Based on the empirical rule, 99,7% of the data will fall within what interval? (231 , 753 ) 15) What is the probability that a randomly selected student will score less than 492 on 16) What proportion of test scores will be greater than 675 on the test? 17) What percentage of scores on the test will be between 330 and 430? 18) Suppose you must score better than 70% of the students who took the test to be ad the University. What must you score to be admitted?try to a certain tributed with estions 12-1 SHORT ANSWER WRITING ASSIGNMENT ) Based on 19) Use StatCrunch to calculate probability for the standard normal distribution and use the C405, values to answer the following. Also, sketch the density curve for each probability statement, a. P(Z $ 1.5) = 3) Based b. P(Z S-1.64) = , P(Z 2 3,46) = 4) Based d, P(-1,24 SZ $ 2,13) = 15) Whi 20) We are interested in the variable X which represents the amount of TV a person watches per week, Use StatCrunch to calculate probabilities for this normal probability distribution, Also, 16) W sketch the density curve for each probability statement. a. P(X 5 5) = 17) V b. P(X 28.5) = c. P(X 2 20) = 18) d. P(10 SX $15) = 21) Once again, we are interested in the variable X which represents the amount of TV a person watches per week, Use StatCrunch to calculate x for this normal probability distribution when given the corresponding probability. Also, sketch the density curve for each. a, P(X S x) =0.95 b. P(X 2 x) = 0,75 22) Draw the normal probability distribution for X, the amount of TV a person watches per week, Remember that the mean is 1 1,7 and the standard deviation is 8.3. Based on the empirical rule identify the following on your graph. a, 68% of the data will fall within what interval? 3, 4 + 0 20 b. 95% of the data will fall within what interval? - 9. 9 40 28.3 c. 99.7% of the data will fall within what interval? - 13, & 10 3%. . 23) Explain the characteristics of the normal distribution, Is there any reason to think that the distribution of TV watching time is not normal? Explain using the drawing you created for question 22 and the histogram for the TV variable as support for your comments, 24) For the TV variable from the student survey give the following and compare the numbers to those given for the population (population mean 1 1.7 and population standard deviation 8,3) a. Mean b. Standard Deviation 25) Explain why it is possible for the population to have a mean of 11.7 and standard deviation 8 3 even if the student survey data does not sunnort this claim Beaduse of P1) Find P(Z S 2.3) 0 . 9 89 276 or O 2) Find P(Z Z -0.3). 8 - 61791 3) Find P(0.6 s Z $ 1.7). or 0. 2 02 68 0 .20 468 4) Find P(Z s-4.9), D. Gaana lor - 1 - 020 A radar unit is used to measure speeds of cars on a motorway, The speeds are normally distributed with a mean of 70 miles per hour and a standard deviation of 10, Use this information to answer questions 5-11, 5) Based on the empirical rule, 68% of the data will fall within what interval? ( 8 0 1 6 0 ) 6) Based on the empirical rule, 95% of the data will fall within what interval? ( 5 0 , 90) 7) Based on the empirical rule, 99,7% of the data will fall within what interval? (yo, 10 0) 8) What percentage of cars will be driving at a speed of 80 miles per hour or faster? 9) What is the probability that a randomly selected car will be driving at a speed less than 55 miles per hour? 10) What proportion of cars are driving between 75 and 85 miles per hour? 1 1) How fast are the top 5% of cars driving