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STATISTICS ASSIGNMENT 1. Determine the mean, median and the mode for the following 1, 2, 3, 4, 4, 7 2. Find the mean, mode and the standard deviation for the following frequency distribution showing student IQ (picture yourself at the bottom!): 3. Find the mean and standard deviation for the following graph: 4. What do each of the following signify? Small standard deviation Large standard deviation Standard deviation of zero 5. If Z is a random variable with a standard normal distribution: determine P(-0.62<Z<0.75) if P(Z<a) = 0.8 determine “a”. 6. If X is a random variable with normal distribution determine P(-3X9), if 4 and 10 if P(Xb)=0.6 and 4 and 10 determine “b”. 7. The attendance for a week at the local theatre is normally distributed with a mean of 4 000 and a standard deviation of 500. What percentage of attendance figures fall between 3 600 and 4 600 people? 8. A provincial Math exam has a mean of 68 and a standard deviation of 13.2. If 30 000 students take the exam and a score of 49 or less fail, how many students fail the exam? 9. A normal random variable X has a mean of 80. If the probability that X is less than 72 is 15%, what is the standard deviation of X? 10. A test to a large group of students approximates the normal curve. The mean is 70 with a standard deviation of 8. If 8% of the students receive A’s and 16% receive B’s, what is the minimum mark needed to receive a B? 11. A fair die is rolled 100 times. Use a normal approximation to calculate the probability of rolling: 20 fours at most 20 fours less than 20 fours between 15 and 22 fives, exclusive between 15 and 22 fives, inclusive 12. If the failure rate for first-year calculus students in university is 40%, find the probability that 8 or fewer students in a class of 30 will fail. 13. A baseball player’s batting average is .300; find the probability of getting 25 or more hits in the next 100 times at bat. 14. The probability that a tire manufactured will be defective is 4%. With 180 tires, what is the probability that no more than 6 are defective? 15. Find the mean and standard deviation for: a – 2b, a, a + 2b