SUBJECT: INTRODUCTION TO STATISTICS.
ANSWER THE 5 QUESTIONS. SOLVE AND ANSWER CORRECTLY. Thanks.
Assignment 4 1. The probability that a randomly chosen sales prospect will make a purchase is 0.30. (a) What is the probability that a salesperson who calls on 10 prospects will make (i) fewer than 3 sales? (ii) more than 4? (2 m) (iii) less than 3 or more than 10 sales? (2 m) (3 m) (b) Calculate the expected number of sales, the variance, and the standard deviation associated with making calls on fifty prospects. (3 m) (CLO2:PLO4:C3)(CLO2:PLO7:C3) 2. The number of errors in a book is a Poisson random variable with a mean of 5 errors in 400 pages. (a) What is the probability that there are 7 errors in 400 pages? (2 m) (b) What is the probability that there are less than 9 errors in 400 pages? (2 m) (c) What is the probability that there are no more than 2 errors in 200 pages? (3 m) (d) What is the probability that there are more than 5 errors in 600 pages? (3 m) (CLO2:PLO4:C3)(CLO2:PLO7:C3) 3. Nice Drink Company produces many types of soft drinks, including Cola. The amount of soda in each can of Cola has a normal distribution with a mean of 12 ounce and a standard deviation of 0.50 ounce. What is the probability that a randomly selected can of Cola contains (a) less than 10.50 ounce of cola? (2 m) (b) more than 12.25 ounce of cola? (3 m) (c) less than 10.75 ounce or more than 13.00 ounce of cola? (5 m) (CLO2:PLO4:C3)(CLO2:PLO7:C3) 4 The print on the package of 100- watt General Electric lightbulbs claims that these bulbs I such bulbs have a normal3. Nice Drink Company produces many types of soft drinks, including Cola. The amount of soda in each can of Cola has a normal distribution with a mean of 12 ounce and a standard deviation of 0.50 ounce. What is the probability that a randomly selected can of Cola contains (a) less than 10.50 ounce of cola? (2 m) (b) more than 12.25 ounce of cola? (3 m) (c) less than 10.75 ounce or more than 13.00 ounce of cola? (5 m) (CLO2:PLO4:C3)(CLO2:PLO7:C3) 4. The print on the package of 100- watt General Electric lightbulbs claims that these bulbs have an average life of 800 hours. Assume that the lives of all such bulbs have a normal distribution with a mean of 800 hours and a standard deviation of 50 hours. Let X be the mean life of a random sample of 25 bulbs. (a) It is possible that X is less than 725? Explain. (5 m) (b) Can X more than 825? Justify your answer. (5 m) (c) What can say about the probability of X lies between 785 and 815? (5 m) (CLO3:PLO6:C4)(CLO3:PLO7:C4) 5. The score on math section of SAT for males in year 2020 follows normal distribution with the mean of 500 points and standard deviation of 72 points. A random sample of 36 SAT's male candidates is selected, (a) it is possible that the sample mean score is less than 400 points? Justify your answer. (5 m) (b) it is possible that the sample mean score is more than 635 points? Explain. (5 m) (c) It is very high chance for the sample mean score lies between 485 and 515? Justify (5 your answer. m) (CLO3:PLO6:C4)(CLO3:PLO7:C4) Em
