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Basic Statistics and Probability

Question 2
Construct a frequency distribution (class, tally and frequency) for the data set using the indicated number of classes. In the table, include the midpoint, relative frequencies and cumulative frequencies. Also construct a relative frequency histogram. Number of class: 5 Data set: 14 10 6 4 19 20 11 5 12 18 5 10 13 23 22 3 12 10 5 24 10 19 7 3 23 15 8 21 5 18 10 7 16

Question 3
a. Find the mean, median, and mode of the data set.
18 25 19 19 23 22 19 23 21 19

b. The following frequency distribution shows the number of newspaper subscriptions per household for a sample of 60 households. Find the mean number of subscription per household. Number of newspapers 0 1 2 3 4 5 Frequency 11 20 16 6 5 2

Question 4
a. The mean rate for cable television from a sample of households was $29.50 per month, with a standard deviation of $2.75 per month. Estimate the percent of cable television rates between $24 and $32.25. (Assume that the data set has a bell-shaped distribution.)

b. In 2004 there were 728 "oldies" radio station in the United States. If one station finds that 138 stations have a larger daily audience than it does, what percentile does this station come closest to in the daily audience ranking?

Question 5
An eight-sided die, numbered 1-8, is rolled. Find the probability that the roll results in an even number or a number greater than six. [Hint: Addition rule for not mutually exclusive events]

Question 6
A manager must select 2 people from a list of 13 specialized employees to form a special group. In how many ways can the manager choose to select 2 people? [Hint: Fundamental counting principle]

Question 7
57% of families say that their children have an influence on their vacation destinations. Consider a random sample of six families who are asked if their children have an influence on their vacation destination.
a. Construct a binomial distribution.

b. Find the mean, variance and standard deviation of the distribution.

Question 8
The probability that an individual is left-handed is 0.1. In a class of 30 students, what is the probability of finding at least five left-handers? [Hint: Binomial probability; P(at least 5)=1-{P(0)+P(1)+P(3)+P(4)}]
a. Construct a binomial distribution.

b. Find the mean, variance and standard deviation of the distribution.

Question 9
Find the indicated probabilities.
a. P (z > -0.89)
b. P (0.45 < z < 2.15)

Write the binomial probability as a normal probability using the continuity correction. Binomial Probability Normal Probability
c. P ( x &#8804; 56) P ( x < ? )
d. P ( x = 69 ) P ( ? < x < ? )

Question 10
The world's smallest mammal is the Kitti's hog-nosed bat, with a mean weight of 1.5 grams and a standard deviation of 0.25 grams. Assuming that the weights are normally distributed, find the probability of randomly selecting a bat that weighs
a. Between 1.0 grams and 2.0 grams.
b. Between 1.6 grams and 2.2 grams.
c. More than 2.2 grams.

Solution Summary

The solution gives the details of computing basic statistics like mean, median, mode and probability.

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