Download Ch. 6 Worksheet

1) Matching - Vocabulary
____a. Normal distribution
1. As sample size  , dist. of sample means
approaches a normal distribution
2. Obtained when repeatedly draw samples
from same population
3.  = 0,  = 1
4. Total area under curve = 1, vertical height  0
5. Represents x by an interval from x -.5 to
x+.5
____b. Uniform distribution
____c. Density curve
____d. Standard normal dist.
____e. Sampling distribution
of sample means
____f. Central limit theorem
____g. Standard error of the
mean
____h. Continuity correction
6.  X
7. Distribution is symmetric, bell-shaped
8. Every random variable is equally likely
For #’s 2, 3, 4: Assume that the readings on a thermometer are normally distributed with a mean
of 0°C and a standard deviation of 1.00°. A thermometer is randomly selected and tested. Draw a
sketch and find the probability of each reading in degrees.
2) Between 0 and 2.00
3) Between -2.0 and 0
4) Between -1.73 and .48
For #’s 5,6: Find the indicated probability where z is the reading in degrees:
5) P (z > 1.8)
6) P (-1.5 < z < 2.8)
For #’s 7, 8, 9: Find the indicated percentile.
7) Find P 40 (the 40th percentile)
8) Find D 20 (the 20th percentile)
9) Find Q 2 (the 50th percentile)
10) A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a
mean of 200 and a standard deviation of 50.
i.
ii.
Find D6 (the tenth decile)
If 40 different applicants are randomly selected, find the probability
that their mean is above 215.
11) In one region, the September energy consumption levels for single-family homes are found
to be normally distributed with a mean of 1050 kwh and a standard deviation of 218 kwh.
(a) For a randomly selected home, find the probability that the September energy
consumption level is between 1050 kwh and 1250 kwh.
a. _________
(b) For a randomly selected home, find the probability that the September energy
consumption level is below 1200 kwh.
b. __________
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(c) For a randomly selected home, find the probability that the September energy
consumption level is above 1175 kwh.
c. __________
(d) Find P45 (the 45th percentile).
d. __________
(e) If 50 different homes are randomly selected, find the probability that their mean
energy consumption level for September is greater than 1075.
e. __________
For #12-13 only : Estimate the indicated probability by using the normal distribution as an
approximation to the binomial distribution.
12) In a study of the causes of death, it was found that 52% of all Americans die from heart
disease. Find the probability that in a group of 500 randomly selected Americans, at least
275 die from heart disease.
___________
13) The Worthington Pottery Company manufactures beer mugs in batches of 120 and the
overall rate of defects is 5%. Find the probability of having more than 6 defects in a batch.
___________
14) Replacement times for CD players are normally distributed with a mean of 7.1 years and a
standard deviation of 1.4 years. Find the replacement time separating the top 45% from the
bottom 55%.
_________
15) A genetics experiment involves a population of fruit flies consisting of 1 male named Mike
and 3 females named Anna, Barbara, and Chris. Assume that two fruit flies are randomly
selected with replacement.
a) List the 16 possible samples, find the proportion of females in each sample, then
use a table to describe the sampling distribution of the proportions of females
(Hint: See Table 6-3 in your book).
b) Find the mean of the sampling distribution.
c) Is the mean of the sampling distribution [from part (b)] equal to the population
proportion of females? Does the mean of the sampling distribution of proportions
always equal the population proportion?
16) This data set includes heights (in inches) of randomly selected women:
66.2, 76.6, 68.7, 70.8, 717
Construct a normal probability plot for these five values and determine whether they appear to
come from a population that is normally distributed and explain why the sample does/does not
appear to be normal (remember: the population distribution need not be exactly normal, but it
must be a distribution that is basically symmetric with only one mode).
17) What kind of distribution emerges when you graph the outcomes for rolling a die? (Hint:
What are the outcomes for rolling a die? What are the probabilities for each roll of the die?)
Draw the graph, then determine the following probabilities:
a) Rolling higher than a five
b) Rolling between a two and a four (inclusive)
c) Rolling less than or equal to a three
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