1) Jack weighs 160 pounds and his sister weighs 110 pounds. If the mean weight for men his age is 175 with a standard deviation of 14 pounds and the mean weight for women is 145 with a standard deviation of 10 pounds, determine whose weight is closer to “average.” Write your answer in terms of z-scores and areas under the normal curve.
2) Explain the difference between a population and a sample. In which if these is it important to distinguish between the two in order to use the correct formula? mean; median; mode; range; quartiles; variance; standard deviation.
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Get Help Now!3) The following numbers represent the weights in pounds of six 7-year old children in Mrs. Jones’ 2nd grade class.
{25, 60, 51, 47, 49, 45}
Find the mean; median; mode; range; quartiles; variance; standard deviation.
4) The Student Services office did a survey of 500 students in which they asked if the student is part-time or full-time. Another question asked whether the student was a transfer student. The results follow.
Transfer Non-Transfer Row Totals
Part-Time 100 110 210
Full-Time 170 120 290
Column Totals 270 230 500
a) If a student is selected at random (from this group of 500 students), find the probability that the student is a transfer student. P (Transfer)
b) If a student is selected at random (from this group of 500 students), find the probability that the student is a part time student. P (Part Time)
c) If a student is selected at random (from this group of 500 students), find the probability that the student is a transfer student and a part time student. P(transfer part time).
d) If a student is selected at random (from this group of 500 students), find the probability that the student is a transfer student if we know he is a part time student. P(transfer | part time).
e) If a student is selected at random (from this group of 500 students), find the probability that the student is a part time given he is a transfer student. P(part time | transfer)
f) Are the events part time and transfer independent? Explain mathematically.
g) Are the events part time and transfer mutually exclusive. Explain mathematically.
5) How do you recognize a binomial experiment?
6) How do you recognize a Poisson experiment?
7) How do you recognize a normal distribution?
8) How do you recognize a discrete distribution?
9) If a normal curve is continuous how are we able to use it for countable random variables as well?
10) Which of the following represent continuous distributions?
a) The lengths of fish in a certain lake. —
b) The number of fish in a certain lake. —
c) The diameter of 15 trees in a forest. —
d) How many trees are on a farmer’s acre. . —
11) On a dry surface, the braking distance (in meters) of a certain car is a normal distribution with mu = 45.1 m and sigma = 0.5 m.
a) Find the braking distance that corresponds to z = 1.8
b) Find the braking distance that represents the 91st percentile.
c) Find the z-score for a braking distance of 46.1 m
d) Find the probability that the braking distance is less than or equal to 45 m
e) Find the probability that the braking distance is greater than 46.8 m
f) Find the probability that the braking distance is between 45 m and 46.8 m.
12) To predict the annual rice yield in pounds we use the equation
where x1 represents the number of acres planted (in thousands) and where x2 represents the number of acres harvested (in thousands) and where r2 = .94.
a) Predict the annual yield when 3200 acres are planted and 3000 are harvested.
b) Interpret the results of this r2 value.
c) What do we call the r2 value?
13) What type of relationship is shown by this scatter plot?
14) What values can r take in linear regression? Select 4 values in this interval and describe how they would be interpreted.
15) Does correlation imply causation?
16) What do we call the r value.
17) If we have data with min = 2; Q1 = 10; median = 12; Q3 = 15; and max = 21; draw a box and whisker.
18) If we have the following data
34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66
draw a stem and le
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