b 2 Heres the fivenumber summary for the distribution of ci

b =

2. Here\'s the five-number summary for the distribution of cigarette taxes (in cents) among the 50 states in the United States.

Minimum = 2.6, Q1 = 35, Median = 62, Q3 = 110, Maximum = 205

(a) About what PROPORTION of the states have cigarette taxes greater than the following?

(i) greater than 35 cents?

(ii) greater than $1.10?

(b) Between what two values are the middle 50% of the observations found?

(c) Find the interquartile range. Interpret it.

The IQR provides the range within one standard deviation of the mean.
The IQR provides the range for the upper half of the data.    
The IQR provides the range for the middle half of the data.
The IQR provides the range for the lower half of the data.

(d) Based on the summary, do you think that this distribution was bell shaped? If so, why? If not, why not, and what shape would you expect?

Yes, the five number summary is fairly evenly spaced.
Yes, the five number summary is very spread out.    
No, the distribution appears skewed to the left.
No, the distribution appears skewed to the right.

Solution

(1) b=-0.006

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(2)

(i) greater than 35 cents?

Since Q1 = 35 which means the 25% of the data, the proportion is 1- 25% = 0.75%

Answer: 75%
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(ii) greater than $1.10?

Since Q3 = 1.10 which means the 75% of the data, the proportion is 1-75% = 25%

Answer: 25%

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(b) Between what two values are the middle 50% of the observations found?

Q1 = 35 and Q3 = 110 (cents)
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(c) Find the interquartile range. Interpret it.

interquartile range= Q3-Q1=110-35 =75 cents

The IQR provides the range for the middle half of the data.

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(d) Based on the summary, do you think that this distribution was bell shaped? If so, why? If not, why not, and what shape would you expect?

Answer: No, the distribution appears skewed to the right.