# Statistics Problem Set: Frequency Distribution

Problem 1. Use the following data set. The data set represents incomes (in thousands of dollars) of 20 employees at an engineering firm.

50, 48, 46, 59, 44, 43, 35, 59, 48, 53,

46, 59, 52, 48, 51, 59, 53, 51, 53, 52

(a) Find the range, mean, median, and mode of the data set.

(b) Make a frequency distribution for the data set using 5 classes. Include class midpoints, frequencies, and relative frequencies.

(c) Make a relative frequency histogram using the frequency distribution in (b).

(d) Determine which class has the greatest relative frequency and which has the least.

Problem 2. The table shows the results of a survey in which 622 men and 644 women ages 25 to 46

were asked if they like Coke or Pepsi.

Men Women Total

Likes Pepsi 325 284 609

Likes Coke 297 360 657

Total 622 644 1266

(a) Find the probability that a randomly selected person likes Pepsi.

(b) Given that a randomly selected person is male, find the probability that the person likes coke.

(c) Given that a randomly selected person likes Pepsi, find the probability that the worker is a female.

(d) Are the events "likes Coke" and "being male" independent or dependent? Explain.

Problem 4. Scores for a statistics exam are normally distributed, with a mean of 80 and a standard deviation of 10. Students scoring in the top 6% of the class are offered the opportunity to take an advanced statistics class. What is the lowest score you can earn and still be eligible to take the advance class?

Problem 5. You randomly select 20 supermarkets and measure the temperature of their coolers. The

sample mean temperature is 43:0 F with a sample standard deviation of 2:0. Find the 95% confidence interval for the mean temperature. Assume the temperatures are approximately normally distributed.

#### Solution Preview

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Problem 1:

(a) Range: max-min=59-35=24.

Mean: (35+43+44+...+59)/20=50.45

Median: (51+51)/2=51

Mode: 59 (appears most times, 4 times)

(b) (see attached)

Class Frequency Midpoint Relative frequency

35-39 1 37 0.05

40-44 2 42 0.1

45-49 5 ...

#### Solution Summary

The expert examines frequency distribution problem sets.