For problems 17 and 18, assume that cans of coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.12 oz. (17) Find the probability that a single can of coke has at least 12.06 oz. Express your answer as a decimal rounded to four decimal places. (SHOW WORK) FINAL ANSWER:

(18) Find the probability that a case of 36 cans have a mean of at least 12.06 oz. Express your answer as a decimal rounded to four decimal places. HINT: think of a sampling distribution for samples of 36 and first find the standard error, which is the standard deviation of a sampling distribution.

Construct the confidence interval for the population mean mu. cequals0.90​, x overbar equals 6.8​, sigmaequals0.2​, and nequals59

A cellphone provider has the business objective of wanting to estimate the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced cost. Data are collected from a random sample of 500 subscribers. The results indicate that 135 of the subscribers would upgrade to a new cellphone at a reduced cost.
a. Construct a 99% confidence interval estimate for the population proportion of subscribers that would upgrade to a new cellphone at a reduced cost.

b. How would the manager in charge of promotional programs use the results in (a)?

• Which regression coefficients (unstandardized or standardized) do you compare to determine the most important predictor variable in the model? Comparing these regression coefficients, would you compare the regression coefficients of all of the predictor variables in the model or just the regression coefficients of the significant predictor variables? After comparing the regression coefficients, how do you know which of the predictor variables is most important?

ccording to a study done by a university​ student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267 . Suppose you sit on a bench in a mall and observe​ people's habits as they sneeze. ​(a) What is the probability that among 10 randomly observed individuals exactly 8 do not cover their mouth when​ sneezing? ​(b) What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when​ sneezing? ​(c) Would you be surprised​ if, after observing 10 ​individuals, fewer than half covered their mouth when​ sneezing? Why?

1. In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities
It is estimated that 3.4% of the general population will live past their 90th birthday. In a graduating class of 750 high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a) 15 or more will live beyond their 90th birthday

(b) 30 or more will live beyond their 90th birthday

(c) between 25 and 35 will live beyond their 90th birthday

(d) more than 40 will live beyond their 90th birthday

2. Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 45.4 months and a standard deviation of 7.7 months.

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.)


(b) If Quick Start does not want to make refunds for more than 13% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

Express the confidence interval 743.8 < μ < 794.6 in the form of ¯ x ± M E . ¯ x ± M E = ±

2. Let x be the number of years after 2007 and y represent the number of students enrolled at WWCC. Answer the following given the data that enrollment was 2055 in the year 2007, 2244 in 2008, 2512 in 2009, 2715 in 2010, and 2765 in 2011.

(a) Find the least-squares line for the data using Excel and submit your file in Canvas.

(b) Using partial derivatives, verify the formula you obtained in Excel.

(c) Find the least-squares error E

The R2 value is an important guide when judging the relationship between two quantities. If you performed linear 2DStats calculations on the original non-linearized data y versus t explain how the value of R2 would help you spot such a mistake

I don't understand how to approach this question but the value is

Many boxed cake mixes include special high-altitude baking instructions. One would like to investigate that, on an average, cakes take longer to bake at high altitudes. A consumer group made several similar cakes in nine-inch rounded pans in Denver and Miami, and carefully recorded the time to bake (in minutes). The data is given as follows:

Baking Times at High Altitude 22.8 30.0 27.3 30.3 28.3 31.1 27.0 26.8 26.3 29.1 23.5 26.2 29.2 23.0

Baking Times at Low Altitude 25.1 25.6 24.9 23.7 25.5 22.4 24.7 24.2 25.6 24.8 23.9 24.4 24.7 24.4 26.4 24.7 24.7 26.8 24.9 24.3

(a)Draw side-by-side boxplots for low and high altitudes. Write a short description about what you observe from the boxplots by examining them individually and contrasting them with regard to measures of center, variability and shapes.

(b)Make a quantile-quantile plot of the data with a 45 degree line added to it. What does the plot tell you about the baking times at the low and high altitudes?

Assume the random variable X is normally​ distributed, with mean mu=49 and standard deviation sigma=7. Find the 10 th percentile.

Suppose the maximum temperature T on any day in Brisbane in January follows a normal distribution with expectation 31 ◦C (degrees Celsius) and standard deviation 2 ◦C. Any temperature above 35 ◦C is deemed dangerous for older people. Using a ta- ble of the normal distribution or otherwise, find the probability that the temperature in Brisbane reaches a dangerous level on any day in January.

Suppose the expected temperature increases by an amount δ due to global warming, while the standard deviation remains the same. What is the smallest δ that will lead to a 5-fold increase in the probability from the previous question?

Instead of a table you may use R or Python to compute probabilities and quantiles. In R, use the functions pnorm and qnorm. In Python, you may use norm.cdf and norm.ppf, as in

     from scipy.stats import norm
     p = norm.cdf(2.0)      # probability
     q = norm.ppf(0.97725)  # quantile

6.2.38 Big Babies: The Centers for Disease Control and Prevention reports that 25% of baby boys 6-8 months old in the United States weigh more than 20 pounds. A sample of 16 babies is studied. (Use Minitab where applicable.)

a.         What is the probability that exactly 5 of them weigh more than 20 pounds?

b.         What is the probability that more than 6 weigh more than 20 pounds?

c.         What is the probability that fewer than 3 weigh more than 20 pounds?

d.         Would it be unusual if more than 8 of them weigh more than 20 pounds?

e.         What is the mean number who weigh more than 20 pounds in a sample of 16 babies aged 6-8 months?

f.          What is the standard deviation of the number who weigh more than 20 pounds in a sample of 16 babies ages 6-8 months?

A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the​ exam, scores are normally distributed with mu equals 517. The teacher obtains a random sample of 2200 ​students, puts them through the review​ class, and finds that the mean math score of the 2200 students is 524 with a standard deviation of 118 . Complete parts​ (a) through​ (d) below. ​(a) State the null and alternative hypotheses. Let mu be the mean score. Choose the correct answer below. A. Upper H 0 : mu less than 517 ​, Upper H 1 : mu greater than 517 B. Upper H 0 : mu equals 517 ​, Upper H 1 : mu not equals 517 C. Upper H 0 : mu greater than 517 ​, Upper H 1 : mu not equals 517 D. Upper H 0 : mu equals 517 ​, Upper H 1 : mu greater than 517 Your answer is correct. ​(b) Test the hypothesis at the alpha equals 0.10 level of significance. Is a mean math score of 524 statistically significantly higher than 517 ​? Conduct a hypothesis test using the​ P-value approach. Find the test statistic. t 0 equals2.78 ​(Round to two decimal places as​ needed.) Find the​ P-value. The​ P-value is 0.003 . ​(Round to three decimal places as​ needed.) Is the sample mean statistically significantly​ higher? No Yes Your answer is correct. ​(c) Do you think that a mean math score of 524 versus 517 will affect the decision of a school admissions​ administrator? In other​ words, does the increase in the score have any practical​ significance? ​No, because the score became only 1.35 ​% greater. Your answer is correct. ​Yes, because every increase in score is practically significant. ​(d) Test the hypothesis at the alpha equals0.10 level of significance with nequals 350 students. Assume that the sample mean is still 524 and the sample standard deviation is still 118 . Is a sample mean of 524 significantly more than 517 ​? Conduct a hypothesis test using the​ P-value approach. Find the test statistic. t 0 equals1.11 ​(Round to two decimal places as​ needed.)