Practice Exam1
1. TRUE or FALSE: Circle either T or F.
(a) T F If a distribution is skewed right, the median should be larger than the mean.
(b) T F A statistic is a numerical summary of a population.
(c) T F Categorical variables take numerical values for which arithmetic operations such as addingand averaging make sense.
(d) T F For a normal distribution, an observation with a z-score of -1.5 is less unusual than anobservation with a z-score of 1.
e) T F If the population distribution is normal, the sample sizemust be at least 30 to ensure that the sampling distribution follows a normal distribution.
2. The UNICEF report \Progress for Children" (April, 2005) included data on the percentage of
primary-school age children who were enrolled in school for 20 countries in Northern Africa. A
stem and leaf plot of this data set is given below.
(a) Using this stem and leaf plot, describe the distribution in terms of shape, center, spread, and
possible outliers.
(b) Find the five-number summary of this data set.
(c) What is the name of the graphical display of the five-number summary?
(d) Of the numerical summaries below, choose one that best represents the center (label with \C")and one that best represents the spread (label with \S") of the data set.
mode
range
mean
interquartile range
standard devation
variance
median
3. A certain standardized test has scores with a normal distribution having mean of 20 and astandard deviation of 5. Several prospective test takers want to know what score they need toget so that they are in a certain predetermined percentile. Assume all scores on this exam onlytake integer values. Therefore all scores should be rounded to the nearest integer. Report anypercentages as a decimal with 4 decimal places.
(a) What score places a student at the 75th percentile?
(b) What score does a student need to get such that 33% of the students scored below it?
(c) What scores bound the center/middle 60% of students?
(d) Joe scored a 34 on this exam. What percent of students scored above Joe?
4. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. Use the 68-95-99.7 rule to answer the following questions.
- How short are the shortest 2.5% of all pregnancies?
c. Suppose a woman has an expected due date 218 days after her policy began. What is the probability that she conceived the child after her policy began?
4. A PC magazine asks all of its readers to participate in a survey of their satisfaction with different brands of computer systems and peripherals. In the 2004 survey, the magazinereported that the average rating assigned by 225 readers to a Kodak compact digitalcamera was 7.5.identify the (a) individual, (b) population, (c) parameter, (d) sample, (e)statistic, (f) sampling method, (g) mention and explain any source of bias.
2. Suppose that we randomly select a sample of 64 measurements from a population having a
mean equal to 20 and a standard deviation equal to 4.
(a) Describe the shape of the sampling distribution of the sample mean x. Do we need to
make any assumptions about the shape of the population? Why or why not?
(b) Find the mean and the standard deviation of the sampling distribution of the sample
mean.
(c) Can you find the probability that a single measurement will be greater than 21? If so,
what is the probability?
(d) Calculate the probability that we will obtain a sample mean greater than 21.