The lengths of pregnancies in a small rural village are normally distributed with a mean of 261 days and a standard deviation of 13 days.

In what range would you expect to find the middle 68% of most pregnancies?
Between  and .

If you were to draw samples of size 31 from this population, in what range would you expect to find the middle 68% of most averages for the lengths of pregnancies in the sample?
Between  and .

Enter your answers as numbers. Your answers should be accurate to 1 decimal places.

A pharmaceutical company is testing a new drug to increase memorization ability. It takes a sample of individuals and splits them randomly into two groups: group 1 takes the drug, group 2 takes a placebo. After the drug regimen is completed, all members of the study are given a test for memorization ability with higher scores representing a better ability to memorize. Those 21 participants on the drug had an average test score of 21.85 (SD = 4.22) while those 28 participants not on the drug (taking the placebo) had an average score of 20.94 (SD = 6.504). You use this information to perform a test for two independent samples with hypotheses Null Hypothesis: μ1 = μ2, Alternative Hypothesis: μ1 ≠ μ2. What is the test statistic and p-value? Assume the population standard deviations are equal. Question 14 options: 1) Test Statistic: -0.558, P-Value: 0.5795 2) Test Statistic: 0.558, P-Value: 0.2898 3) Test Statistic: 0.558, P-Value: 0.7103 4) Test Statistic: 0.558, P-Value: 0.5795 5) Test Statistic: 0.558, P-Value: 1.7103

As of 2012, the proportion of students who use a MacBook as their primary computer is 0.36. You believe that at your university the proportion is actually greater than 0.36. The hypotheses for this test are Null Hypothesis: p ≤ 0.36, Alternative Hypothesis: p > 0.36. If you randomly select 20 students in a sample and 10 of them use a MacBook as their primary computer, what is your test statistic and p-value?

Question 11 options:

In a packing plant, one of the machines packs jars into a box. A sales rep for a packing machine manufacturer comes into the plant saying that a new machine he is selling will pack the jars faster than the old machine. To test this claim, each machine is timed for how long it takes to pack 10 cartons of jars at randomly chosen times. Given a 95% confidence interval of (0.72, 6.72) for the true difference in average times to pack the jars (old machine - new machine), what can you conclude from this interval?

Question 8 options:

The lengths of pregnancies in a small rural village are normally distributed with a mean of 263 days and a standard deviation of 13 days.

In what range would you expect to find the middle 50% of most pregnancies?
Between  and .

If you were to draw samples of size 50 from this population, in what range would you expect to find the middle 50% of most averages for the lengths of pregnancies in the sample?
Between  and .

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 195.3 cm and a standard deviation of 1 cm. For shipment, 24 steel rods are bundled together.

Note: Even though our sample size is less than 30, we can use the z score because
1) The population is normally distributed and
2) We know the population standard deviation, sigma.

Find the probability that the average length of a randomly selected bundle of steel rods is between 194.8 cm and 194.9 cm.


Enter your answer as a number accurate to 4 decimal places.

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.962 g and a standard deviation of 0.313 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 48 cigarettes with a mean nicotine amount of 0.899 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 48 cigarettes with a mean of 0.899 g or less.  
Enter your answer as a number accurate to 4 decimal places.

Based on the result above, is it valid to claim that the amount of nicotine is lower?

• No. The probability of obtaining this data is high enough (greater than a 5% chance) to have been a chance occurrence.
• Yes. The probability of this data is unlikely (less than a 5% chance) to have occurred by chance alone.

R_{o = rate of transmission}

Probability of infection = R_o /N

Herd Immunity Threshold = 1 – 1/R_o

1a) In some flu seasons Influenza has an R_o = 2. If 100 people are exposed to an individual that is infected, what is the probability that one of them becomes infected?

1b) What percentage of the 100 people would need to be vaccinated to reach the Herd Immunity Threshold (HIT) in which the R_o is less than 1?

1c) Currently, with an estimated R_o of around 4 for COVID-19 What percentage of the 100 people would need to be vaccinated to reach the Herd Immunity Threshold (HIT) in which the R_o is less than 1?

Show all manual calculations and provide commentary to your answers.

A company that manufactures bookcases finds that the average time it takes an employee to build a bookcase is 10 hours with a standard deviation of 2 hours. A random sample of 64 employees is taken. What is the likelihood that the sample mean will be 9 hours or more? The average grade point average (GPA) of undergraduate students in New York is normally distributed with a population mean of 2.5 and a population standard deviation of .5. Compute the following, showing all work:

(I) The percentage of students with GPA's between 1.3 and 1.8 is: (a) less than 5.6% (b) 5.7% (c) 5.9% (d) 6.2% (e) 6.3% (f) 6.6% (g) 7.3% (h) 7.5% i) 7.9% (j) more than 8%.

(II) The percentage of students with GPA's below 2.3 is:

(III) Above what GPA will the top 5% of the students be (i.e., compute the 95th percentile):

(IV) If a sample of 36 students is taken, what is the probability that the sample mean GPA will be between 2.60 and 2.75

4. At the end of the Halloween Festival, the organizers estimated that a family of participants spent in average of $45.00 with a standard deviation of $10.00. If 49 participants (49 = size of the sample) are selected randomly, what's the likelihood that their mean spent amount will be within $4 of the population mean? (mean +/- 4)

FDA food contamination guidelines allow for pineapple juice to contain up to 15% mold and still be shipped out. In practice, it is assumed that pineapple juice is okay to be shipped out; a batch is only discarded if there is statistically significant evidence that it contains more than the allowed amount of mold.

(a) Write the appropriate null and alternative hypotheses for this approach to the situation.

(b) Which of the following is the consequence of making a type I error?

• A batch of pineapple juice meets the guidelines, but is discarded.

• A batch of pineapple juice fails to meet the guidelines, but is shipped out.

• A batch of pineapple juice meets the guidelines, and is shipped out.

• A batch of pineapple juice fails to meet the guidelines, and is discarded.

(c) Which of the following is the consequence of making a type II error?

• A batch of pineapple juice meets the guidelines, but is discarded.

• A batch of pineapple juice fails to meet the guidelines, but is shipped out.

• A batch of pineapple juice meets the guidelines, and is shipped out.

• A batch of pineapple juice fails to meet the guidelines, and is discarded.

(d) Which level of significance (α) minimizes the probability that a batch of pineapple juice gets shipped out when it fails to meet the guidelines?

0.1 0.05 0.01

Data 1 and Data 2 represent two samples from your production on Monday and Tuesday of this week. Calculate the P-value when comparing the population averages of these two groups.

Please include Excel calculations.

Data 1

Data 2

Data Below represent a sample. What is the probability of the population mean to be above 263.1?

Please include Excel Calculations.

An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is x Overscript bar EndScripts equals 1.44 and the sample standard deviation is s = 0.27. Find a 99% lower confidence bound on the true Izod impact strength. Assume the data are normally distributed. Round your answer to 3 decimal places. less-than-or-equal-to

A banking executive studying the role of trust in creating customer advocates has determined that 41 %41% of banking customers have complete​ trust, 47 %47% of banking customers have moderate​ trust, and 12 %12% have minimal or no trust in their primary financial institution. Of the banking customers that have complete​ trust, 66 %66% are very likely to recommend their primary financial​ institution; of the banking customers that have moderate​ trust, 16 %16% are very likely to recommend their primary financial​ institution; and of the banking customers that have minimal or no​ trust, 1 %1% are very likely to recommend their primary financial institution. Complete parts​ (a) and​ (b) below.

A. Compute the probability that if a customer indicates he or she is very likely to recommend his or her primary financial​ institution, the banking customer also has complete trust.

B) Compute the probability that a banking customer is very likely to recommend his or her primary financial institution.

sickle cell anemia is a hereditary medical condition affecting red blood cells that are thought to protect against malaria, a debilitating parasitic infection of the liver and blood. that would explain why the sickle cell traits found in people who originally came from Africa, where malaria is widespread, a study in Africa tested 543 children for the sickle cell also for malaria infection in all 25% of the children had sickle cell and 6.6% of the children had both sickle cell and malaria. overall 34.6% of the children had malaria

Make a Venn diagram with the information provided. use it to answer the following questions

a) what is the probability that a child has either malaria or sickle cell?

b) what is the probability that a child has neither malaria or sickle cell, round to 3 decimal places

c) what is the probability that a child has malaria given that the child has the sickle cell trait

d) what is the probability that a child has malaria given that child does not have the sickle cell trait

e) Are the events sickle cell trait and malaria independent? what might that tell you about the relationship between sickle cell and malaria

The Bureau of Meteorology of the Australian Government provided the mean annual rainfall (in millimeters) in Australia 1983–2002 as follows (http://www.bom.gov.au/ climate/change/rain03.txt) 499.2, 555.2, 398.8, 391.9, 453.4, 459.8, 483.7, 417.6, 469.2, 452.4, 499.3, 340.6, 522.8, 469.9, 527.2, 565.5, 584.1, 727.3, 558.6, 338.6 Construct a 99% two-sided confidence interval for the mean annual rainfall. Assume population is approximately normally distributed. Round your answers to 2 decimal places. less-than-or-equal-to mu less-than-or-equal-to

Section 8.1 Expanded: Constructing the nonlinear profit contribution expression

Let P_S and P_D represent the prices charged for each standard golf bag and deluxe golf bag respectively. Assume that “S” and “D” are demands for standard and deluxe bags respectively.

S = 2250 – 15P_S                                                                                                                                                  (8.1)

D = 1500 – 5P_D                                                                                                                                                   (8.2)

Revenue generated from the sale of S number of standard bags is P_S*S. Cost per unit production is $70 and the cost for producing S number of standard bags is 70*S.

So the profit for producing and selling S number of standard bags = revenue – cost = P_SS – 70S                      (8.3)

By rearranging 8.1 we get                            

15P_S = 2250 – S or

                                P_S = 2250/15 – S/15 or

                                P_S = 150 – S/15                                                                                                                                                  (8.3a)

Substituting the value of P_S from 8.3a in 8.3 we get the profit contribution of the standard bag:

                                (150 –S/15)S – 70S = 150S – S²/15 – 70S = 80S – S²/15                                                                      (8.4)

Revenue generated from the sale of D number of deluxe bags is P_D*D. Cost per unit production is $150 and the cost for producing D number of deluxe bags is 150*D.

So the profit for producing and selling D number of deluxe bags = revenue – cost = P_DD – 150D                     (8.4a)

By rearranging 8.2 we get                            

5P_D = 1500 – D or

                                P_D = 1500/5 – D/5 or

                                P_D = 300 – D/5                                                                                                                                                   (8.4b)

Substituting the value of P_D from 8.4b in 8.4a we get the profit contribution of the deluxe bags:

                                (300 -D/5)D – 150D = 300D – D²/5 – 150D = 150D – D²/5                                                                 (8.4c)

By adding 8.4 and 8.4c we get the total profit contribution for selling S standard bags and D deluxe bags.

                                Total profit contribution = 80S –S²/15 + 150D – D²/5                                                                         (8.5)

Homework assignment:

Reconstruct new objective function for 8.5 by changing “15P_S” to “8P_S” in 8.1, “5P_D” to “10P_D” in 8.2, cost per unit standard bag from 70 to “70+last two digits of your UTEP student ID” and cost per unit deluxe bag from 150 to 125. Keep other parameter values unchanged. Use up to 2 decimal points accuracy. Substitute your new expression for 8.5 in the excel solver workbook as explained in the class and solve for the optimal combination values for S and D. Submit the printout from the excel solution in either March 02, 2019 or March 4, 2020 class. Instructor will not accept any homework late or submitted outside the class. Make sure you submit the results (just one page excel printout). Write/type your full name (first name first) in upper case, last 4 of your UTEP student ID, and, your new objective function expression (like equation 8.5 above) on the printout. Use S and D instead of b15 or c15 in writing the formulation. If you fail to follow the instructions, you will lose points.

*the last 2 digits of my ID are 61