4. There are 10 keys and only one of them can open a lock. We do not know which key can open the lock, but we will try them one by one until we find the right key. Let X denote the number of times tried to find the right key. (a) What is the p.m.f. of X? (b) What is the C.D.F. of X? (c) What is the mean and variance of X?

Assume that the traffic to the web site of Smiley's People, Inc., which sells customized T-shirts, follows a normal distribution, with a mean of 4.48 million visitors per day and a standard deviation of 900,000 visitors per day. (a) What is the probability that the web site has fewer than 5 million visitors in a single day? If needed, round your answer to four decimal digits, (b) What is the probability that the web site has 3 million or more visitors in a single day? If needed, round your answer to four decimal digits. (e) What is the probability that the web site has between 3 million and 4 million visitors in a single day? If needed, round your answer to four decimal digits. (d) Assume that 85% of the time, the Smiley's People web servers can handle the daily web traffic volume without purchasing additional server capacity. What is the amount of we traffic that will require Smiley's People to purchase additional server capacity? If needed, round your answer to two decimal digits.…

8. Find the value of the standard error of the mean in each of the following cases. (Use the finite Suppose a random sample of size 30 is selected from a population with o = population correction factor if appropriate. Round your answers to two decimal places.) (a) The population size is infinite. (b) The population size is = 30,000. (c) The population size is N = 3,000.

The proportion of vehicles which drive above the speed limit on a freeway is 85%.  Suppose 100 vehicles are randomly clocked. 20 If each speeding vehicle is issued a $185 speeding ticket, the expected value of the ticket amount is $________.   a $15,725               b $14,560               c $13,480               d $12,485

5. A shipment of 24 electric stoves is rejected if three 3 are checked for defects and at least one 1 is found ton be defective. Find the probability that the shipment will be returned if there are actually six stoves that are defectives.

1. Suppose the prices of used cars in the market are normally distributed with a mean of $15,000 and a standard deviation of $7,5000. What is the probability of selecting a car from this market and its priced above $20,000.

The probability distribution for the number of automobiles sold during a day (x) at Bob Iron Motors isas follows. x f(x) 0 0.001 1 0.007 2 0.034 3 0.099 4 0.188 5   6 0.220 7 0.136 8 0.055 9 0.015 10 0.001 17 The probability that 5 automobiles will be sold is,a 0.232b 0.244c 0.257d 0.271

You may need to use the appropriate appendix table to answer this question. Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.) (a) The area to the left of z is 0.9750. 1.8 x (b) The area between O and z is 0.4750. (c) The area to the left of z is 0.7291. (d) The area to the right of z is 0.1271. (e) The area to the left of z is 0.8106. () The area to the right of z is 0.1894.

Question 21 On the average, the amount of money that a customer spends in the store is $40 with a standard deviation $1O. The probability that the total spending of 4 customers in the store is over $170 is closest to 0.1543 0.3085 0.2376 O 0.4013 not able to calculate

The profit for a production process is equal to $1,000 minus two times the number of units produced. The mean and variance for the number of units produced are 50 and 90, respectively. Find the mean and variance of the profit.