Math 4 - Practice with Sample Proportions #2
Name___________________________
1.
At Kingman High School, suppose that 29% of all freshmen fail their first math class.
Principal Sanders decides to replace Ms. McNeil, a math teacher, because 40% of her 107
freshmen math students failed their first math class. What is the probability that a random
sample of this size at Kingman High School would have a failure rate of 40% or higher? Express
your answer to four decimal places.
2.
Passer rating is a numerical grade given to an NFL quarterback based on his performance,
usually in one particular game. It is desired to have a high passer rating. Suppose a normal
population can be made with all passer ratings for quarterbacks in games played from 1991 to
the present. The mean of this data set is 103.5, and its standard deviation is 21.7. In order to
have a passer rating for a game that is higher than 75% of all other quarterbacks, what must
one's passer rating be? Please round your answer to one decimal place.
3.
Consider the data set: {1, 7, 11, 19, 25}.
Provide the sampling distribution of all sample means of size 2 for this data set.
4.
For the last few years, suppose a data set records the number of minutes spent watching
television each day for every teenager in Augusta. The distribution is normal, with a mean of 97
minutes, and a standard deviation of 42 minutes. If 10 teenagers are chosen randomly, what is
the probability they average 90 minutes or fewer of television viewing time? Round your
answer to four decimal places.
5.
A physical fitness association is including the mile run in its secondary-school fitness test. The
time for this event for boys in secondary school is known to possess a normal distribution with a
mean of 450 seconds and a standard deviation of 50 seconds. The fitness association wants to
recognize the fastest 10% of the boys with certificates of recognition (only 10% of boys have a
lower time). What time would the boys need to beat in order to earn a certificate of recognition
from the fitness association?
6.
Suppose that five students paid the following amounts for textbooks this semester:
$80, $104, $120, $128, and $160. Using a sample size of 4, find the sampling distribution
of the sample means.
7.
Kaley and Tyler have applied for admission to the University of Missouri. Kaley is from
Minnesota and has an ACT mathematics score of 30. Tyler is from California and has not taken
the ACT, but his score on the math section of the SAT is 620.
A)What is Kaley's percentile rank on the math section of the ACT if its mean 21,
and its standard deviation is 5 (assume it is normally distributed)? Round to two decimal places.
B)What is Tyler's percentile rank on the math section of the SAT if its mean 500,
and its standard deviation is 100 (normally distributed)? Round to two decimal places.
C)Based on the information in A & B, which student scored relatively higher on his/her
given test?
8.
The number of violent crimes committed in a day possesses a normal distribution with a mean
of 2.8 crimes per day and a standard deviation of 4 crimes per day. A random sample of 100
days was observed, and the sample mean number of crimes for the sample was calculated to
be 3.3. What is the probability that any sample of 100 days would have an average amount of
violent crimes committed of 3.3 or lower? Round to four decimal places.
9.
The annual precipitation amounts in a certain mountain range are normally distributed with a
mean of 99 inches, and a standard deviation of 14 inches. What is the probability that the mean
annual precipitation during 49 randomly picked years will be more than 101.8 inches? Express
to four decimal places.
10.
A human gene carries a certain disease from the grandmother to the grandchild with a
probability rate of 35%. That is, there is a 35% chance that the grandchild becomes infected
with the disease. Suppose a female carrier of the gene has twenty-nine grandchildren. Assume
that the infections of the twenty-nine grandchildren are independent of one another. Find the
probability that 10 or less of the grandchildren get the disease passed down from their
grandmother. Round to four decimal places.
11.
By 2011, the average household in Georgia owned an average of 4.1 television sets with a
standard deviation of 2.3. A simple random sample was taken of 50 households in Augusta.
What is the probability that any random sample of 50 households would own an average of
between 3 and 4 television sets? Round to four decimal places.
12.
Suppose that 52% of all voters in California are in favor of recalling the California governor. An
exit poll (a common sampling method during elections) sampled 360 random voters as they left
the poll and found that 198 wanted to recall the governor. What is the probability that 198 or
less of the 360 voters who voted in the election want to recall the governor? Express to four
decimal places.
1. .0060 2. 118.0 3. 4,6,9,10,13,13,15,16,18,22 4. .2981 5. 386 6. 108,116,118,122,128
7. A)96.41% B)88.49% C)Kaley 8. .8944 9. .0808 10. .4801 11. .3779 12. .8729