Example Practice Problems for STAT 509 Final Exam 1. The newest Boeing 787-9 Dreamliner is designed to be 206 feet in length. The manufacturing process for assembling the 787-9 follows a normal distribution with mean 205.8 feet and standard deviation 0.5 feet. a) If the specification for the 787-9 Dreamliner is 206 feet plus or minus 1 foot, or (205’ , 207’), what percentage of the assembled airplanes are beyond the specifications? Draw a Normal Graph of the data. (5) b) Find the 90% percentile of all 787-9 airplanes in terms of length? Show on a Normal Graph (5) c) Find the probability that a random sample of 5 airplanes exceeds a mean of 206.5 feet. Draw a Normal Graph of the data. (5) 2. A group of 300 people were surveyed. Their marital status was recorded along with answers to several questions. One question asked was whether “Friends and social life” or “Job or primary activity” contributes most to their general well-being. The results from this question appear in the table below. Single (never married) Married Widowed or divorced Friends and social life 47 59 56 Job or primary activity 33 61 44 Find the probability that a randomly selected person chose “Friends and social life”. Find the probability that a randomly selected person is “Married” and chose “Friends and social life”. Find the probability that a randomly selected person chose “Friends and social life” given the person is “Married”. Are the events chose “Friends and
Since in a normal distribution, the curve is symmetrical, skewness can affect the accuracy to which normal distribution can be applied to a data set. To determine how close the distribution of the weight of the AFL population is to being normal, the degree of skewness was found as a large degree of skewness would reduce the practicality of applying normal distribution to the data set.
Assuming our mean is still 400, but a new standard deviation of 1.667 based on a six-sigma process, we find the proportion of the rubber extruded that is within our specifications by calculating the probability that rubber sent through the extruder will be outside our limits:
The area under the curve to the left of the unknown quantity must be 0.7 (70%). So, we must first find the z value that cuts off an area of 0.7 in the left tail of standard normal distribution. Using the cumulative probability table, we see that z=0.53.
2. In order to determine the average amount spent in November on Amazon.com a random sample of 144 Amazon accounts were selected. The sample mean amount spent in November was $250 with a standard deviation of $25. Assuming that the population standard deviation is unknown, what is a 95% confidence interval for the population mean amount spent on Amazon.com in November?
(c) The mean of the sample and the value of Z with an area of 5% in the left tail.
4. Calculate the following measures of central tendency for the set of cube measurement data. Show your work or explain your procedure for each.
If John gets an 90 on a physics test where the mean is 85 and the standard deviation is 3, where does he stand in relation to his classmates? (he is in the top 5%, he is in the top 10%, he is in the bottom 5%, or bottom 1%)
5) Describe how the normal range for any given measurement is obtained. Explain why published values for normal ranges may differ and why these values must be continually checked and updated.
7. The data set for this problem can be found through the Pearson Materials in the Student Textbook Resource Access link,
Knowing this information, you need to first tell me, and then show this in your graph:
There is a decline in first marriages where neither partner has been married before. But there is a growing number of remarriages, in which one or both partners have been divorced; these marriages constitute 15% of all marriages in 1971 and 40% in 1996.
Plot 3 is located on the slope and had the greatest mean height with 28.22m. This was 13% and 20% taller than the next tallest plot and the stand mean height respectively. The plots heights have a range of 19.75 to 31.77 (12.02) and this is the largest range out of all the plots.
C. Retired Seniors. People who belong in this group have ages above 65. Most of them have been living together with their partner for a long time and over the years have built a strong, solid relationship. They have medium/high level of education and are currently retired, so most of their time is spent enjoying each other’s company. Even though they may not have a very fruity income at the moment, they have accumulated a
When couples divorce a range of things, such as social environment, demographic, and life decisions can influence divorce. These sentiments were mirrored by Barbara Dafoe Whitehead and David Popenoe as they noted that divorce is determined based on the background characteristics that spouses bring with them to the marriage. The research then goes further to offer more statistics on those experiencing divorce. It indicates if a person is well educated with a reasonable income, from a sound family, religious, and marry after age 25 without having a baby first, your chances of divorce are considered to be very low.
b) z = -1.21 ( find 0.5 – 0.1131 = 0.3869 in the normal table)