Question

What is the chance a randomly selected employee would get a non-zero bonus amount? What is the chance a randomly selected employee would get at least $6000? What is the expected bonus value of the bonus amounts? What are the variance and standard deviation of the bonus amount? Binomial Suppose according to past data for a small boutique, about 30% of the customers who walk into the store purchase at least one item. Today 10 individual customers walked into the store while you are there. How many of these 10 customers do you expect would by at least one item? (hint: expected value formula) What is the chance that exactly 3 of the customers would purchase at least one item? What is the probability that no more than 3 customers would purchase at least one item? (Hint: sketch a table for the number of people who would purchase at least one item out of the 10. You do not need to put in all the probabilities, just all the values of X. For which values of X would you have to add the probabilities? Student who were in my BUS 90 class are familiar with this problem. Feel free to help your fellows on Canvas discussion this weekend.) Uniform A package delivery service breaks up its shipping charges into weight classes, where the package weights are uniformly distributed WITHIN each weight class. Suppose one of the shipping classes is 12 to 15 lbs. What proportion of packages in this class would weigh less than 14 lbs? (draw the distribution as I did in class) What proportion would weigh more than 12.5 lbs? What would the average weight for a package in this class be? Uniform distribution The scheduled commuting time on the Long Island Railroad from Glen Cove to New York City is 65 minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes. What is the probability that the commuting time will be less than 70 minutes? (draw the graph and shade in the appropriate area!) What is the probability that the commuting time will be between 65 and 70 minutes? (draw the graph and shade in the appropriate area!) What is the probability that the commuting time will be greater than 65 minutes? (draw the graph and shade in the appropriate area!) What is the expected (average) commuting time? Uniform again A study of the time spent shopping in a supermarket for a market basket of 20 specific items showed an approximately uniform distribution between 20 and 40 minutes. What is the probability that the shopping time will be between 25 and 30 minutes? (draw the graph and shade in the appropriate area!) What is the probability that the shopping time will be less than 35 minutes? (draw the graph and shade in the appropriate area!) What is the probability that the shopping time will be more than 27 minutes? (draw the graph and shade in the appropriate area!) What is the mean shopping time? Practice with normal – draw graphs with correct area shaded in and proper x and z axes. Use the tables I handed out in class. If you do not have such tables, google a set to use. To have tables similar to those I gave you, go back to the assignment where one is attached.) The fill amount in 2-liter soft drink bottles is normally distributed with a mean of 2.0 liters and a mean of 0.05 liters. If bottles contain less than 95% of the listed net content (i.e., less than 1.90 liters) the manufacturer may be subject to penalty by the state office of consumer affairs. Bottles that have a net content above 2.10 liters may cause excessive spillage upon opening. What is the probability that a randomly selected bottle will contain: Between 1.90 and 2.00 liters? Between 1.90 and 2.10 liters? Below 1.90 liters or above 2.10 liters? At least how much soft drink (in liters) is contained in 99% of the bottles? (Draw the graph and try to see whether lower 99% and upper 99% works best to figure this out). 99% of the bottles contain an amount that is between which two values, symmetric about the average? Binomial again About 40% of the residents aged 25 and older in San Jose CA have completed a college degree. If you were to do a very small marketing research survey of 5 people, what is the chance you would get exactly 2 people with college degrees (assuming everyone was 25 or older)? What is the chance you would get at least two people with college degrees in your sample? (Hint: make a table of all the possible numbers of people out of 5 with college degrees, and calculate the probabilities for the relevant numbers. ). What is the chance you would get at most two people with college degrees in your sample? (same hint as above) How many college graduates do you expect to have in your sample of 5?

Answer 1

Let X is a random variable shows the number of cutomers out of 10 who walk into the store purchase at least one item. Here X has binomial distribution with parameters n=10 and p=0.30.

What is the chance that exactly 3 of the customers would purchase at least one item?

The expected value is:

What is the probability that no more than 3 customers would purchase at least one item?

Following table shows the required probabilites:

X	P(X=x)
0	0.028247525
1	0.121060821
2	0.233474441
3	0.266827932
total	0.649610718

So,