Section 2.2 HW
What is the shape of the distribution shown? Graph tall on the left and short on the right
Skewed right
What is the shape of the distribution shown? Pyramid shaped
Symmetric and bell-shaped
The accompanying table shows the tax, in dollars, on a pack of cigarettes in 30 randomly selected cities. (a) Construct a frequency distribution. Use a first class having a lower class limit of 0 and a class width of 0.50. (b) Construct a relative frequency distribution. Use a first class having a lower class limit of 0 and a class width of 0.50 (d) Construct a relative frequency histogram. Choose the correct graph below. (e) Describe the shape of the distribution. (f) Repeat parts (a)dash-(e) using a class width of 1. Construct a frequency distribution. (g) Does one frequency distribution provide a better summary of the data than the other? Explain.
a) 0-.49 = 4, 0.50-0.99 = 9, 1.00-1.49 = 5, 1.50-1.99 = 4, 2.00-2.49 = 3, 2.50-2.99 = 2, 3.00-3.49 = 2, 3.50-3.99 = 0, 4.00-4.49 = 1 b) 0-0.49 = 0.13 0.50-0.99 = 0.3 1.00-1.49 = 0.17 1.50-1.99 = 0.13 2.00-2.49 = 0.1 2.50-2.99 = 0.07 3.00-3.49 = 0.07 3.50-3.99 = 0 4.00-4.49 = 0.03 c) graph D d) graph A e) skewed right f) 0-0.99 = 13 1-1.99 = 9 2-2.99 = 5 3-3.99 = 2 4-4.99 = 1 0-0.99 = 0.43 1-1.99 = 0.3 2-2.99 = 0.17 3-3.99 = 0.07 4-4.99 = 0.03 graph D; graph C; skewed right g) Both distributions have a similar shape, so either works well.
To predict future enrollment in a school district, fifty households within the district were sampled, and asked to disclose the number of children under the age of five living in the household. The results of the survey are presented in the table. (a) Construct a relative frequency distribution of the data. (b) What percentage of households has two children under the age of 5? (c) What percentage of households has one or two children under the age of 5?
a) 0= .3 1= .28 2= .3 3= .1 4= .02 b) 30% c) 58%
An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The frequency histogram to the right gives the results. (a) What was the most frequent outcome of the experiment? (b) What was the least frequent? (c) How many times did we observe a 3? d) How many more 8's were observed than 9's? (e) Determine the percentage of time a 3 was observed. (f) Describe the shape of the distribution.
a) 7 b) 2 c) 5 d) 4 e) 5% f) Bell-shaped
The data to the right represent the number of customers waiting for a table at 6:00 P.M. for 40 consecutive Saturdays at Bobak's Restaurant. (a) Are these data discrete or continuous? Explain. (b) Construct a frequency distribution of the data. (c) Construct a relative frequency distribution of the data. (d) What percentage of the Saturdays had 4 or more customers waiting for a table at 6:00 P.M.? e) (e) What percentage of the Saturdays had 6 or fewer customers waiting for a table at 6:00 P.M.? (f) Construct a frequency histogram of the data. Choose the correct histogram below. (g) Construct a relative frequency histogram of the data. Choose the correct histogram below. (h) Describe the shape of the distribution. Choose the correct answer below.
a) The data are discrete because there are a finite or countable number of values. b) 1-3 = 10 4-6 = 13 7-9 = 11 10-12 = 5 13-15 = 1 c) .25, .325, .275, .125, .025 d) 75% e) 57.5 f) graph D g) graph C h) The distribution is skewed right because the right tail is longer than the left tail.
A researcher wanted to determine the number of televisions in households. He conducts a survey of 40 randomly selected households and obtains the data in the accompanying table. (a) Are these data discrete or continuous? Explain. (b) Construct a frequency distribution of the data.
a) The given data are discrete because they can only have whole number values. b) 2,12,15,8,2,1 c) .05, .3, .375, .2, .05, .025 d) 20% e) 7.5% f) B g) D h) skewed right