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Q1. Waiting in Line: A Wendy's manager performed a study to determine a probability distribution for the number of people, X, waiting in line during lunch. The results were as follows: (a) Verify that this is a discrete probability distribution. (b) Compute and interpret the mean of the random variable X. (c) Compute the standard deviation of the random variable X. (d) What is the probability that eight people are waiting in line for lunch? Q2. Smokers: According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Ten smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.
(a) Explain why this is a binomial experiment. (b) Find and interpret the probability that exactly 8 of them started smoking before 21 years of age. (c) Find and interpret the probability that fewer than 8 of them started smoking before 21 years of age. (d) Find and interpret the probability that at least 8 of them started smoking before 21 years of age. (e) Find and interpret the probability that between 7 and 9 of them, inclusive, started smoking before 21 years of age. Q3. You Explain It! Miles per Gallon: Elena conducts an experiment in which she ?lls up the gas tank on her Toyota Camry 40 times and records the miles per gallon for each ?ll-up. A histogram of the miles per gallon indicates that a normal distribution with a mean of 24.6 miles per gallon and a standard deviation of 3.2 miles per gallon could be used to model the gas mileage for her car.
(a) The ?gure represents the normal curve with m = 24.6 miles per gallon and s = 3.2 miles per gallon. The area under the curve to the right of x = 26 is 0.3309. Provide two interpretations of this area. (b) The ?gure at the top of the next column represents the normal curve with m = 24.6 miles per gallon and s = 3.2 miles per gallon. The area under the curve between x = 18 and x = 21 is 0.1107. Provide two interpretations of this area. Q4. Assume that the random variable X is normally distributed, with mean m = 50 and standard deviation s = 7. Find the 90th percentile for X. Q5. Smokers: According to the Information Please Almanac, 80% of adult smokers started smoking before they were 18 years old. Suppose 100 smokers 18 years old or older are randomly selected. Use the normal approximation to the binomial to:
(a) approximate the probability that exactly 80 of them started smoking before they were 18 years old. (b) approximate the probability that at least 80 of them started smoking before they were 18 years old. (c) approximate the probability that fewer than 70 of them started smoking before they were 18 years old.
if a data set has correlation coefficient equal to 0.9 which of the following is necessarily true about the data points
Suppose there are two samples of size 6 and 7, with a rank sum of 58 in the sample of size 6. Using the Wilcoxon rank sum test, evaluate the significance of the results, assuming there are no ties.
An analyst working at BC Statistics is compiling a report on the use of the internet at home. In 1997, 250 randomly selected people were asked about the average amount of time spent on the internet per week.
Determine the percent of the days is the price between $38.00 and $40.00?
Giving Null and Research Hypothesis
If random sample of thirty six customer transactions points out that sample mean withdrawal amount is $172, is there evidence to think that population mean withdrawal amount is no longer $160? Determine the mean of data above?
Use the SPSS output to determine if there is sufficient evidence to conclude that Sally bakes a better pie than Pat (i.e., the average rating for Sally at her church is higher than the average rating for Pat at her church).
Since over 10,000 students in his state took the Math SAT, he can show that the P-value for testing whether the mean score in his state is more than the national average of 480 is less than 0.0001. What we can conclude from this?
Conduct a hypothesis test at the 6% level of significance to determine whether there is evidence that the true mean fill volume for all jugs of softener differs from 120 ounces.
Find the value of the annuity after 15 years and find the interest.
This project has put a lot of light on the necessity of sound doctrine and its importance. One would think that if people attended church more, they would be more in tune with God and sound doctrine
The chief aim of sampling is to be able to select a. simple random samples b. a sample whose statistics will accurately portray an unknown population parameter
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