Brianna Delgado
June 11, 2015
STAT: 1020
Assignment #3: Chapter 5 and Chapter 6
CHAPTER 5
3. From the mid-1960s to the early 1990s, there was a slow but steady decline in SAT scores. For example, take the verbal SAT. The average in 1967 was about 543; by 1994, the average was down to about 499. However, the AD stayed close to 110. The drop in averages has a large effect on the tails of the distribution. (a) Estimate the percentage of students scoring over 700 in 1967. (b) Estimate the percentage of students scoring over 700 in 1994.
You may assume that the histograms follow the normal curve.
Answer:
(a) 5.5%
(b) 2.3%
5. In HANESS, the men age 18 and over had an average height of 69 inches and an SD of 3 inches. The histograms is show below, with a normal curve. The percentage of men with heights between 66 inches and 72 inches is exactly equal to the area between (a) and (b) under (c). This percentage is approximately equal to the area between (d) and (e) under the (f). Fill in the blanks.
For (a), (b), (d), and (e), your options are: 66 inches, 72 inches, -1, +1.
For (c) and (f), your options are: normal curve and histogram.
Answer:
a) -1
b) +1
c) Normal curve
d) 66 inches
e) 72 inches
f) histogra
7. Among freshmen at a certain university, scores on the Math SAT followed the normal curve, with an average of 550 and an SD of 100.
(a) Approximately, what is the percentile rank for a student who scored 400 on the Math SAT? And Why?
(b) Approximately, what is the 75th
7. Question : In a frequency distribution such as a bell-shaped curve, what does the vertical height of the curve indicate?
18. Suppose that the scores of architects on a particular creativity test are normally distributed. Using a normal curve table, what percentage of architects have Z scores:
b) What number of credit hours students in this sample are taking would be at the 20th percentile?
Use the data in the table above and answer the following questions in the space provided below:
16) According to a college survey, 22% of all students work full time. Find the mean for the number of
7. This practice problem uses the data contained in the file named Ch. 3 Data Set 3. There are two variables in this data set. The data sets can be found through the Sage Materials in the Student Textbook Resource Access link, listed under Academic Resources. Using IBM® SPSS® software, compute all of the measures of variability you can for height and weight. Copy and paste the output from IBM® SPSS® into this worksheet.
Cynthia has always performed well in her job, and has received good performance appraisals. She has been denied a promotion to a more lucrative sales position because she was told she “is not attractive enough” for the position. Cynthia is likely a victim of
The standard deviation was 20.86. For the SAT Verbal, the mean was 595.05, the median was 598.5, and the mode was 590. The standard deviation was 16.197. For the Test Anxiety Questionnaire, the mean was 24.25, the median was 23.5, and bimodal of 20 and 37. The standard deviation was 8.098.
A life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 71 years and a standard deviation of 3.5 years. What proportion of the plan participants are expected to see their 75th birthday? Note: Write your answers with two places after the decimal, rounding off as appropriate.
Rohrer stated the number was roughly 80 out of a class of 200. After the meeting, I asked Dr. Newcome for clarification. He stated the number taking the SATs has traditionally fallen within 42 and 47 percent. You with me so far? So, if 80 students take the SATs, and 87.7 percent pass, then roughly 70 students are passing. This means only 35 percent of ALL students are meeting the SAT benchmark for College Readiness.
At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. Above what value do 2.5% of the sample means fall? ANSWER: 1.057
34. Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000. a. If we select a random sample of 50 households, what is the standard error of the mean? b.
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.
In this mathematical circumstance, it is appropriate to use the Normal Model with this data distribution because of how roughly symmetric and unimodal. The summary statistics for the OB Math SAT scores are as follow: the number of values is 287, the mean of the data is 553.62369, the standard deviation is of approximately 65.984512, the median of the data is 540, the range of the data is 390, the minimum value is 360, the maximum value is 750, the first quartile of the data is 510, and the second quartile of the data is 590. To calculate the percent of students that had an SAT math score higher than 560, I used the z-score formula which is z-score= raw score- mean/ standard deviation and plugged the values for each variable. After