Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fullfil each week is 2. (a) What is the probability that in a given week the plant cannot fulfil all the placed orders? (b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

The age of a students in a class is a normal random variable. There are 80 students in our class. I select 9 students randomly and calculate the mean of their ages (sample mean). I repeat this experiment 1,000,000 times. Then I calculate the mean and standard deviation of the 1,000,000 sample means that I measured; the calculated values are 22 and 4, respectively. What is the probability that the age of a randomly selected student in the class is below 20?

There are two ways for a concrete truck to go from a ready-mixed concrete plant to the construction site. The first way is direct, for which the mean and standard deviation of travel time are 30 min and 5 min, respectively. The second way is through Town A. The mean and standard deviation of travel time between the plant and Town A are 14 min and 5 min, respectively. The mean and standard deviation of travel time between Town A and the construction site are 14 min and 6 min, respectively. If the total travel time is above 45 min, the concrete in the truck will go bad. Calculate the probability that the concrete goes bad for both cases of choosing the direct and indirect ways. Assume travel time has a normal distribution.   

Historically, the population average waiting time to check out of a supermarket has been 4 minutes. Recently, in an effort to reduce the waiting time, the supermarket experimented with a recommendation system that generates real-time information to management the on number of cashiers to staff. The system involves infrared cameras that measure the amount of body heat in the checkout area of the store. The data from the cameras are feed in to an analytical software system that determines how many customers are waiting in line. After reviewing the results of the analytical software system, management determines how many cashiers to staff from the existing employees in other service areas of the store. A test of the new recommendation was conducted on a sample of 100 customers, and their mean waiting time to check out was 3.10 minutes, with a sample standard deviation of 2.5 minutes.

a. At the 0.05 level of significance determine if there is evidence to conclude that the recommendation system helped management to significantly reduce customer waiting time.

b. What technique did you use to determine your answer in part a?

c. Give the details necessary to demonstrate the technique to an audience.

d. What assumptions did you make in part a?

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfil each week is 2. (a) What is the probability that in a given week the plant cannot fulfil all the placed orders? (b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

Consider the value of t such that 0.05 of the area under the curve is to the right of t. Step 2 of 2: Assuming the degrees of freedom equals 20 , select the t value from the t table.

Boys and Girls: Suppose a couple plans to have two children and the probability of having a girl is 0.50.

(a) What is the sample space for the gender outcomes?

{bb, bg, gg}

{b,g}    

{bb, bg, gb, gg}

{bb, gg}

(b) What is the probability that the couple has one boy and one girl?

(c) What is the probability that the couple will have at least one girl?

(d) What is the probability that the couple will have no girls?

There are two ways for a concrete truck to go from a ready-mixed concrete plant to the construction site. The first way is direct, for which the mean and standard deviation of travel time are 30 min and 5 min, respectively. The second way is through Town A. The mean and standard deviation of travel time between the plant and Town A are 14 min and 5 min, respectively. The mean and standard deviation of travel time between Town A and the construction site are 14 min and 6 min, respectively. If the total travel time is above 45 min, the concrete in the truck will go bad. Calculate the probability that the concrete goes bad for both cases of choosing direct and indirect ways. Assume travel time has a normal distribution.

An archaeologist discovers only seven fossil skeletons from a previously unknown species of horse. Reconstructions of the skeletons of these seven horses show the shoulder heights (in centimeters) to be:

132 141 143 107 123 145 163

Find a 95% confidence interval for the mean shoulder height. Show work.

Consider the following time series data.

Excel File: data17-35.xls

b. Show the four-quarter and centered moving average values for this time series (to 3 decimals if necessary).

c. Compute seasonal indexes and adjusted seasonal indexes for the four quarters (to 3 decimals).

The amount of corn chips dispensed into a 13​-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 13.5 ounces and a standard deviation of 0.4 ounces. Suppose 50 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 50 bags exceeded 13.6 ounces. Round to four decimal places.

1. A chemist in interested in determining the weight loss of a particular compound as a function of the amount of time the compound is exposed to the air. The data below give the weight losses associated with settings of the exposure time.

                  Weight Loss (in pounds)           Exposure Time (in hours)

        ____________________________________________________

                          4.0                                                  4

                           6.0                                                  5

                                2.0                                             3

                           .                                                    .

                                 .                                                        .

                           9.0                                                  6

        ____________________________________________________

         Use the computer printout (below) to answer the questions.

* * * *   L I N E A R            R E G R E S S I O N   * * * *

Dependent Variable:     Weight Loss

Independent Variable: Exposure Time

                         Analysis of Variance

                              Sum of       Mean                             p

Sources     df      Squares     Squares          F          Value

-----------------------------------------------------------------------

Regression     1      70.417       70.417           F_obs         .000

Residual       10       SS_res         MS_res       

-----------------------------------------------------------------------

Total            11     84.917

---------- Variables in the Equation -----------

Variable                   B         SE B          t           p Value   

Exposure Time    2.167       0.311       6.969       0.000      

(Constant)          -5.833       1.745      -3.343       0.007

         8       points

          (a)      Why do we need to use linear regression analysis in this study?

TYPE YOUR ANSWERS BELOW:

               (1)

                  ______

               (2)

                  ______

         (b)     Briefly describe the concept of least-squares regression line.

TYPE YOUR ANSWER BELOW:

                  ______

          (c)     Why this study is called simple linear regression analysis instead

Using standard deviation and variance, what if we wanted to compare the variation in body lengths of great white sharks and greater short-horned lizards? What measure of variation would you suggest we use, and why?

This question is a conceptual portion of R programming.

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 4.56 million visitors per day and a standard deviation of 800,000 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.

(c) 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 web traffic that will require Smiley’s People to purchase additional server capacity? If needed, round your answer to two decimal digits. ______ million visitors per day

A single observation of a random variable (that is, a sample of size n = 1) having a geometric distribution
is used to test the null hypothesis θ = θ0 against the alternative hypothesis θ = θ1 for θ1 < θ0. The null
hypothesis is rejected if the observed value of the random variable is greater than or equal to some positive
integer k. Find expressions for the probabilities of type I and type II errors.