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Chapter 5: Q2 (page 195)
Is the random variable given in the accompanying table discreteor continuous? Explain.
Number of Girls x | P(x) |
0 | 0.063 |
1 | 0.25 |
2 | 0.375 |
3 | 0.25 |
4 | 0.063 |
The variable x is a discrete random variable.
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For 100 births, P(exactly 56 girls) = 0.0390 and P(56 or more girls) = 0.136. Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question?
In Exercises 15鈥�20, assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n = 8 trials, each with probability of success (correct) given by p = 0.20. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is at least 4.
In Exercises 25鈥�28, find the probabilities and answer the questions.
Whitus v. Georgia In the classic legal case of Whitus v. Georgia, a jury pool of 90 people was supposed to be randomly selected from a population in which 27% were minorities. Among the 90 people selected, 7 were minorities. Find the probability of getting 7 or fewer minorities if the jury pool was randomly selected. Is the result of 7 minorities significantly low? What does the result suggest about the jury selection process?
Identifying Binomial Distributions. In Exercises 5鈥�12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.
LOL In a U.S. Cellular survey of 500 smartphone users, subjects are asked if they find abbreviations (such as LOL or BFF) annoying, and each response was recorded as 鈥測es,鈥� 鈥渘o,鈥� or 鈥渘ot sure.鈥�
The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.
0 0 1 2 17 28 21 8
a. Find the mean.
b. Find the median.
c. Find the mode.
d. Find the range.
e. Find the standard deviation.
f. Find the variance.
g. Use the range rule of thumb to identify the values separating significant values from those that are not significant.
h. Based on the result from part (g), do any of the planets have a number of moons that is significantly low or significantly high? Why or why not?
i. What is the level of measurement of the data: nominal, ordinal, interval, or ratio?
j. Are the data discrete or continuous?
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