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1. As part of their customer service assessment, a manufacturer compiled the table below showing wait times (rounded to the nearest minute) for calls to their appliance help center. Wait time (min) 1 2 3 4 5 6 7 8 9 10 Number 16 55 87 101 87 63 42 20 16 13 a. What is P(X = 1)? b. What is P(X= 5)? c. What is P(X = 10)? d. What is the value of the cumulative distribution function for this random variable in the range 1 sx< 2? e. What is the value of the cumulative distribution function for this random variable in the range 5 SX < 6? f. What is the value of the cumulative distribution function for this random variable in the range 9 S x < 10? g. What is the mean of the random variable in this problem? h. What is the variance for the random variable in this problem? i. Assume that five people independently place a service call to the appliance help center What is the probability that the waiting time of exactly one person is less than or equal to 4 min? j. Assume that five people independently place a service call to the appliance help center. What is the probability that exactly two people wait more than 4 min? k. Assume that five people independently place a service call to the appliance help center. What is the probability that at least one person waits more than 4 min?

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

The queuing time at an airline check-in has a population mean h = 13 minutes and variance o2 = 16 minutes2. Suppose that n = 27 passengers were randomly selected from this population. They were interviewed and reported the queued times. Let x̄ defines the sample mean of n observations. Answer the followings:

a) Define your random variable X.

b) Define the sampling distribution of sample mean (indicate a reason and give the name of the distribution, the parameters and sketch it.

c) What is the probability that a sample mean is at most 11 minutes. Please skecth the problem and show all details of your answer.

d) Suppose that for n = 27 passengers, the sample mean is observed as x̄= 10 minutes. Based on part c, can we claim that the population mean queuing time is less than 13 minutes.

e) Construct a 95% acceptance region for sample mean of queing time (i.e., u + za x f) Interpret the result obtained in parte and skecth the control chart.

People enter a restaurant and check their hat at the coat check, but since the worker is new, he makes the mistake of throwing all the hats in a pile. When the patrons return to claim their hats at the end of the evening, the worker gives each person a random hat from the pile.  

1. What is the probability that no one receives their own hat back if there are only 2guests?

2. What is the probability that no one receives their own hat back if there are 3 guests?

3. What is the probability that no one receives their own hat back if there are 4 guests?

4. What is the probability that no one receives their own hat back if there are 8 guests?

5.What is the probability that no one receives their own hat back if there are 10 guests?

To solve, build a systematic method. For example, one way you could do it is by defining several events, where P_i = the number of ways of a person i to recive their hat correctly, and then the number of ways that at least one person to recive their hat is the union of P_1,...,P_n; finally, you can count this using inclusion/exlusion, then count the complement to finish the problem. 

 

(14 marks) Fortune magazine publishes a list of the world’s billionaires each year. We will examine the top 97 of the 1992 list. Their wealth, age, and geographic location (Asia, Europe, Middle East, United States, and Other) are reported. Wealth is a right-skewed variable, so we will consider the natural logarithm log wealth to be the response and will see if age and geographic location are predictors.
(a) (2 marks) Let
Ebe a variable that is 1 if the person is from Europe and 0 otherwise,
Mbe a variable that is 1 if the person is from the Middle East and 0 otherwise,
Obe a variable that is 1 if the person is from the “Other” region and 0 otherwise,
and
Ube a variable that is 1 if the person is from the United States and 0 otherwise.
State a linear model for the mean of log wealth that includes age and the above 4
geographic variables. Call this the full model.
(b) (5 marks) The SSY for these data is 28.3351 and the SSE from fitting the full model
is 27.0461. Use this information to construct an ANOVA table. Your table should
include columns for Source, df, SS, MS and F, and should include rows for the model
(full model), residual and total.
(c) (2 marks) In addition to the full model, the reduced model that includes only an
intercept and age is fit. What is the null hypothesis being considered by fitting these
two models? (Refer to quantities defined in your model.)
(d) (3 marks) The SSM from the reduced model is 59.7. Calculate an F-statistic to test the hypothesis of part (c). State the degrees of freedom for the F-distribution
you would compare this statistic to. (You do not need to calculate the p-value or actually test the hypothesis.)
(e) (1 mark) Using terminology from class, name the kind of Ftest that the statistic in part (d) corresponds to.
(f) (1 mark) If the null model for these data is compared to the model that includes an
intercept and age, what are the results?

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