Please refer to the following table:

Number of Cellular Phones  in Household:

DECILE
1 - 1.00
2 - 1.00
3 - 1.00
4 - 1.00
5 - 2.00
6 - 2.00
7 - 3.00
8 - 3.00
9 - 4.00

(a) How many cellular phones does a household have at the 42nd percentile? 
(b) How many cellular phones does a household have at the 3rd quartile? 
(c)90 percent of respondents have ______ cellular phones or fewer.

(a) To determine the number of cellular phones at the 42nd percentile, we need to find the decile that corresponds to that percentile.

Looking at the given table, we can see that the 42nd percentile falls between decile 4 and decile 5.

The value at decile 4 is 1.00, and the value at decile 5 is 2.00.

To find the number of cellular phones at the 42nd percentile, we can calculate the weighted average between the two deciles.

Weighted average = value at decile 4 + (percentile - lower percentile) * (value at decile 5 - value at decile 4)

Weighted average = 1.00 + (0.42 - 0.40) * (2.00 - 1.00)

Weighted average = 1.00 + 0.02 * 1.00

Weighted average = 1.00 + 0.02

Weighted average = 1.02

Therefore, a household at the 42nd percentile would have approximately 1.02 cellular phones.

(b) To determine the number of cellular phones at the 3rd quartile, we need to find the decile that corresponds to that quartile.

The 3rd quartile is the same as the 75th percentile.

Looking at the given table, we can see that the 75th percentile falls between decile 7 and decile 8.

The value at decile 7 is 3.00, and the value at decile 8 is 3.00.

So, a household at the 3rd quartile would have 3.00 cellular phones.

(c) To determine the number of cellular phones that 90 percent of respondents have or fewer, we need to find the decile that corresponds to the 90th percentile.

Looking at the given table, we can see that the 90th percentile falls between decile 8 and decile 9.

The value at decile 8 is 3.00, and the value at decile 9 is 4.00.

So, 90 percent of respondents have 3.00 or fewer cellular phones.

To determine the number of cellular phones at a specific percentile or quartile, we need to understand the concept of percentiles and quartiles.

(a) The 42nd percentile represents the value below which 42% of the data falls. To find the number of cellular phones at the 42nd percentile, we can look for the corresponding value in the table. Based on the given table, it shows that the 42nd percentile lies between the values of 2.00 and 3.00. While the exact value is not provided, we can estimate that it falls between those two numbers.

(b) The 3rd quartile represents the value below which 75% of the data falls. To find the number of cellular phones at the 3rd quartile, we can look for the corresponding value in the table. Based on the given table, the 3rd quartile lies between the values of 3.00 and 4.00. Similar to the previous question, the exact value is not provided, but it falls between those two numbers.

(c) To determine the number of cellular phones that 90 percent of respondents have or fewer, we need to look for the value at the 90th percentile. However, the table only provides information up to the 9th decile, so we don't have a specific value for the 90th percentile. In this case, we cannot determine the exact number of cellular phones for this question based on the given table.

In summary, for questions (a) and (b), we can estimate the range of possible values based on the provided table, but we cannot determine the exact value without additional information. For question (c), the information in the table is insufficient to determine the exact number of cellular phones.