Chapter 8: Q.6 (page 477)

The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys $200$ people. The sample mean is $8.2$ minutes. There is a known standard deviation of $2.2$ minutes. The population distribution is assumed to be normal.
Identify the following:
a. $x ¯$ = ___
b. $σ$ = _
c. $n$ = ___

Short Answer

Expert verified

The value of

a). $\bar{x} = 8.2$

b). $σ = 2.2$

c). $n = 200$

Step by step solution

Part (a) Step 1: Given Information

The sample mean is

8.2

minutes.

Part (a) Step 2: Explanation

The sample mean is the average (or mean) value of a group of numbers drawn from a larger population of numbers, where "population" refers to all relevant data, whether or not it has been gathered.
The sample mean is

8.2

minutes.

Part (b) Step 1: Given Information

There is a known standard deviation of $2.2$ minutes.

Part (b) Step 2: Explanation

The standard deviation is a measurement of a set of values' variation or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are dispersed across a larger range.

There is a known standard deviation of $2.2$ minutes.