An elevator has a placard stating that the maximum capacity is 1328 lb--8 passengers. So, 8 adult male passengers can have a mean weight of up to 1328/8=166 pounds. If the elevator is loaded with 8 male passengers, find the probability that it is overloaded because they have a mean weight greater than 166 lb. (Assume that weights of males are normally distributed with a mean of 173 lb and a standard deviation of 29 lb.) Does this elevator appear to be safe?

The numbers illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1000 and the standard deviation is $60.

820, 880, 940, 1000, 1060, 1120, 1180, are the Distribution of Prices

What is the approximate percentage of buyers who paid between $820 and $1000?
? %

What is the approximate percentage of buyers who paid between $940 and $1000?
? %

What is the approximate percentage of buyers who paid more than $1120?
? %

What is the approximate percentage of buyers who paid between $1000 and $1120?
? %

What is the approximate percentage of buyers who paid between $940 and $1060?
? %

What is the approximate percentage of buyers who paid less than $820?
? %

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150lb and 201lb. The new population of pilots has normally distributed weights with a mean of 158lb and a standard deviation of 34.2 lb.

a. If a pilot is randomly​ selected, find the probability that his weight is between 150lb and 201lb.

b. if the number different pilots are randomly selected, find the probability that their mean weight is between 150lb and 201lb

c. When redesigning the ejection seat, which probability is more relevent ?

The lengths of pregnancies in a small rural village are normally distributed with a mean of 264 days and a standard deviation of 15 days.

In what range would we expect to find the middle 68% of most lengths of pregnancies? Round the answer to one decimal place.

Between and days

If we were to draw samples of size 56 from this population, in what range would we expect to find the middle 68% of most averages for the lengths of pregnancies in the sample? Round the answer to one decimal place.

Between and days

If the joint probability distribution of X1 and X2 is given by: f(X1, X2) = (X1*X2)/36 for X1 = 1, 2, 3 and X2 = 1, 2, 3, find the joint probability distribution of X1*X2 and the joint probability distribution of X1/X2.

A doctor claims that the number of births by day of the week is uniformly distributed. To test this claim, you randomly select 700 births from a recent year and record the day of the week on which each takes place. The table shows the results.

Test the doctor's claim at the significance level a=0.05.

a) What is the assumed proportion of births in each day?(in fractions)

b) State H0 and Ha.

c) What is the degrees of freedom of the test?

d) Calculate the x^2 test statistic.

e) Decide whether to reject the null hypothesis.

g) Interpret the decision in the context of the original claim.

Data collected from two groups of subjects, one used generic drugs(Gen) and the other used Refernce drug(Ref). The average absorption extent for Refernce drug that applied to Nref=78 subjects was Xref=2065, with the SD of Sref=881.8. The average absorption for Generic (Gen) that applied to NGen= 79 subject was XGen=2085 with the SD of SGen=643.5. State HO and H! and test the significance of the differnce between generic and refernce drugs at 95% level.

Need some guidance... thank you

The lengths of pregnancies in a small rural village are normally distributed with a mean of 266 days and a standard deviation of 13 days.

In what range would we expect to find the middle 95% of most lengths of pregnancies? Then Round the answer to one decimal place to find the answer..

Between ? and ? days.

If we were to draw samples of size 38 from this population, in what range would we expect to find the middle 95% of most averages for the lengths of pregnancies in the sample? Then Round the answer to one decimal place to find the answer. .

Between ? and ? days.

]It is widely known that alcohol related car accidents can have a big impact on people’s lives. One widely reported statistic is that the mean number of “years of potential life lost” among men is 32, but it was computed several years ago. Researchers want to know if this statistic has changed since the data were first compiled, with a significance level of 5%. A random sample of 24 alcohol related fatalities from this moth had a mean “years of potential life lost” of 33.8 and a standard deviation of 6 years.

a. [7 points] Construct a confidence interval around the sample mean at 95% Confidence Level.

b. [7 points] Based on the confidence interval, how would you decide about the hypothesis that the mean statistic of “years of potential life lost” has remained the same (at 5% level of significance)?

What is the probability that seven-digit phone number has one or more repeated digits ?

The leading number can not be zero (0).

Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars). Weekly Usage (hours) Annual Maintenance Expense 20 23 17 28 27 36 35 43 39 53 24 37 31 39 38 45 47 58 45 46 Develop the estimated regression equation that relates annual maintenance expense (in hundreds of dollars) to weekly usage hours (to 3 decimals). Expense = + Weekly Usage Test the significance of the relationship in part (a) at a .05 level of significance. Compute the value of the F test statistic (to 2 decimals). The p value is What is your conclusion? Jensen expects the new machine to be used 30 hours per week. What is the expected annual maintenance expense in hundreds of dollars (to 2 decimals)? Develop a 95% prediction interval for the company's annual maintenance expense for this machine (to 2 decimals). ( , ) If the maintenance contract costs $3000 per year, would you recommend purchasing the contract for the new machine in part (c)?

The following table lists the activities needed to complete a project. The first column lists the activities and the “follows” column shows which other activity or activities, (if any), must be completed before these activities can start. The remaining columns give three estimates of the activity duration; the mean duration calculated from these estimates and standard deviation assuming a beta distribution of activity duration.

a) Calculate mean duration and standard deviation for all activities using the beta distribution. (4 points)
  
b) Construct a network diagram for this problem using the mean durations calculated in part (a), calculate the ES (Prec.), LS(Foll.) and the total float for all the activities, and hence identify the critical path . What is the mean completion time for the project? What is the standard deviation of the critical path? (3 0 points)
  
c) What is the 99% confidence interval for the length of the critical path? (4 points)
  
d) Assuming that the probability distribution of the length of the critical path can be approximated by a normal distribution with the mean and standard deviation calculated in part (b), calculate the probability of completing the project within 34 days . (4 points)
  
e) What is the probability that the project will be completed between 38 and 45 days? Show your workings! (4 points)
  
f) Answer the project manager’s question:
“I want to tell the client a project length which I am 89.97% sure that we can meet _- What figure should I give them?" (4 points)

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x over bar​, is found to be 106​, and the sample standard​ deviation, s, is found to be 10. ​(a) Construct a 96​% confidence interval about mu if the sample​ size, n, is 24. ​(b) Construct a 96​% confidence interval about mu if the sample​ size, n, is 19. ​(c) Construct an 80​% confidence interval about mu if the sample​ size, n, is 24. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

Ralph’s bowling scores in a single game are normally distributed with a mean of 120 and a standard deviation of 10.

Lucky Lolly’s bowling scores in a single game a normally distributed with a mean of 100 and standard deviation of 15.

1. Is Lolly or Ralph more likely to score over 165 in a single game? Show your work.
2. Is Lolly or Ralph more likely to score over 130 in a single game? Show your work.