Q2 (8 points) The mean amount purchased by each customer on non-medical mask at Chopper Drug Mart is 23 dollars with a standard deviation of 50 dollars. The population is positively skewed. For a sample of 50 customers, what is the probability that the sample mean is greater than 22 dollars but less than 25 dollars Q3 (8 points) The annual commissions earned by sales representative of York Machine Products Inc. of light machinery, follow the normal distribution. The mean yearly amount earned is 40,000 dollars and the standard deviation is 5000 dollars. The sales manager wants to award the sales representatives who earn the largest commissions a bonus of 8888 dollars. He can award a bonus to 20 percent of the sales representatives. What is the cutoff point between those who earn a bonus and those who do not? Q4 (18 points) If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is a. Within 1.5 standard deviations of its mean value? b. Farther than 2.5 standard deviations from its mean value? c. Between 1 and 2 standard deviations from its mean value? 05 (8 points) There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.1 cm. The second machine produces corks with diameters that are normally distributed with mean 3.04 cm and standard deviation 0.02 cm. Acceptance corks have diameters between 2.9 cm and 3.1 cm. Which machine is more likely to produce an acceptable cork