1. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 252 feet and a standard deviation of 46 feet. We randomly sample 49 fly balls.

(a) If X = average distance in feet for 49 fly balls, then give the distribution of X. Round your standard deviation to two decimal places.

X ~ ____ ( ____ , ____ )

(b) What is the probability that the 49 balls traveled an average of less than 240 feet? (Round your answer to four decimal places.)

____

(c) Find the 70th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)

____ ft

2. Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 146 minutes with a standard deviation of 15 minutes. Consider 49 of the races. Let X = the average of the 49 races.

(a) Give the distribution of X. (Round your standard deviation to two decimal places.)

X ~ ____ ( ____ , ____ )

(b) Find the probability that the average of the sample will be between 144 and 149 minutes in these 49 marathons. (Round your answer to four decimal places.)

(c) Find the 60th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)

___ min

(d) Find the median of the average running times.

___ min

3. In 1940 the average size of a U.S. farm was 174 acres. Let's say that the standard deviation was 57 acres. Suppose we randomly survey 42 farmers from 1940.

(a) In words, define the random variable X.

1. the number of U.S. farms

2. the number of square feet of a U.S. farm

3. the number of acres of a U.S. farm

4. the number of animals on a U.S. farm

(b) In words, define the random variable X.

1. the average number of farms in each state in the United States

2. the average number of square feet of a farm in the sample of 42 farmers

3. the average number of acres of a farm in the sample of 42 farmers

4. the average number of animals on a U.S. farm

(c) Give the distribution of X. (Round your standard deviation to two decimal places.)

X ~ ____ ( ____ , ____ )

(d)The middle 50% of the distribution for X, the bounds of which form the distance represented by the IQR, lies between what two values? (Round your answers to two decimal places.)

_____ acres	(smaller value)
______ acres	(larger value)

4. Salaries for teachers in a particular elementary school district are normally distributed with a mean of $43,000 and a standard deviation of $6,400. We randomly survey ten teachers from that district.

(a)In words, define the random variable X.

the number of teachers in an elementary school in the district

the number of elementary schools in the district

the number of teachers in the district

the salary of an elementary school teacher in the district

(b)Give the distribution of X. (Enter exact numbers as integers, fractions, or decimals.)

X ~ ____ ( ____ , ____ )

(c)In words, define the random variable X.

the sum of all teachers in ten elementary schools in the district

the sum of all districts with ten elementary schools

the sum of salaries of ten elementary school administrators in the district

the sum of salaries of ten teachers in elementary schools in the district

(d)Give the distribution of X. (Round your answers to two decimal places.) X ~ ____ ( ____ , ____ )

(e)Find the probability that the teachers earn a total of over $400,000. (Round your answer to four decimal places.)

____

(f)Find the 90^th percentile for an individual teacher's salary. (Round your answer to the nearest whole number.)

$ _____

(g)Find the 90^th percentile for the sum of ten teachers' salary. (Round your answer to the nearest whole number.) $ _____

(h)If we surveyed 70 teachers instead of ten, graphically, how would that change the distribution in part (d)?

1. The distribution would not change.

2. The distribution would be a more symmetrical normal curve.

3. The distribution would shift to the left.

4. The distribution would become an exponential curve.

5. The distribution would shift to the right.

(i)If each of the 70 teachers received a $3000 raise, graphically, how would that change the distribution in part (b)?

1. The distribution would take a wider shape.

2. The distribution would shift to the right.

3. The distribution would not change.

4. The distribution would shift to the left.

5. The distribution would take a more narrow shape.

5. X ~ N(50, 13). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let X be the random variable of sums.

(a) Give the distribution of X.(Enter an exact number as an integer, fraction, or decimal.)

X ~ ____ ( ____ , ____ )

(b) Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.)

P(X < 50) = ?

(c) Find the 40th percentile. (Round your answer to two decimal places.)

(d) Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.)

P(46 < X < 52) = ?

(e) Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(17 < X < 49) = ?

(f) Give the distribution of X.

X ~ ____ ( ____ , ____ )

(g) Find the minimum value for the upper quartile for X. (Round your answer to two decimal places.)

(h) Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.)

P(1150 < X < 1300) = ?

6. The average length of a maternity stay in a U.S. hospital is said to be 2.4 days with a standard deviation of 0.8 days. We randomly survey 80 women who recently bore children in a U.S. hospital. (a)In words, define the random variable X.

1. the average length of a maternity stay, in days

2. the number of children born in a U.S. hospital

3. the length of a maternity stay in a U.S. hospital, in days

4. the average number of children born in a U.S. hospital

(b)In words, define the random variable X.

1. the average number of children born in a U.S. hospital

2. the length of a maternity stay in a U.S. hospital, in days

3. the average number of women admitted to a hospital

4. the average length of a maternity stay in a U.S. hospital, in days

(c) Give the distribution of X.

(Round your standard deviation to two decimal places.)

X ~ ____ ( ____ , ____ )

(d) In words, define the random variable X.

1. the total number of babies born to all 80 women in the sample

2. the total number of U.S. hospitals

3. the total length of a woman's pregnancy

4. the total number of days of the maternity stays of all 80 women in the sample

(e)Give the distribution of X. (Round your standard deviation to two decimal places.) X ~ ____ ( ____ , ____ )