Question

Find the a. MEAN and b. STANDARD DEVIATION for the data set. Round to two decimal places.

10) Country Number of Television Sets per 100 people
A 124
B 94
C 129
D 109
E 114
A) a. 115
b. 13.69
B)
a. 114
b. 13.69
C)
a. 114
b. 169
D) a. 113
b. 13.69
Provide an appropriate response.
11) If an adult male is told that his height is within 2 standard deviations of the mean of the normal distribution of heights of adult males, what can he assume?
A) His height measurement is in the same range as about 99.7% of the other adult males whose heights were measured.
B) His height measurement is in the same range as about 95% of the other adult males whose heights were measured.
C) He is taller than about 99.7% of the other men whose heights were measured.
D) He is taller than about 95% of the other men whose heights were measured. The scores on a driver's test are normally distributed with a mean of 100. Find the score that is:_____
12) Find the score that is 2 standard deviations below the mean, if the standard deviation is 26.
A) 126
B) 48
C) 152
D) 74
Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid:____
13) between $147,700 and $152,300 if the standard deviation is $2300.
A) 34%
B) 95%
C) 99.7%
D) 68%
14) more than $154,800 if the standard deviation is $2400.
A) 95%
B) 2.5%
C) 47.5%
D) 97.5%
A set of data items is normally distributed with a mean of 60. Convert the data item to a z-score, if the standard deviation is as given. 15) data item: 100; standard deviation:_____
a) 10
b) 40
c) 10
d) 4/3

Answer 1

Explained below.

Explanation:

(10)

The data set is:

S = {124, 94, 129, 109, 114}

The mean and standard deviation are:

`\bar x=(1)/(n)\sum x=(1)/(5)* [124+94+...+114]=114\\\\s=\sqrt{(1)/(n-1)\sum ( x-\bar x)^(2)}`

`=\sqrt{(1)/(5-1)* [(124-114)^(2)+(94-114)^(2)+...+(114-114)^(2)]}\\=\sqrt{(750)/(4)}\\=13.6931\\\approx 13.69`

The correct option is B.

(11)

According to the Empirical 95% of the data for a Normal distribution are within 2 standard deviations of the mean.

So, the adult male's height is in the same range as about 95% of the other adult males whose heights were measured.

The correct option is B.

(12)

Let the score be X.

Given:

μ = 100

σ = 26

`X=\mu-2\sigma`

`=100-(2* 26)\\=100-52\\=48`

The correct option is B.

(13)

Let X be the prices of a certain model of new homes.

Given:
`X\sim N(150000, 2300^(2))`

Compute the percentage of buyers who paid between $147,700 and $152,300 as follows:

`P(147700<X<152300)=P((147700-150000)/(2300)<(X-\mu)/(\sigma)<(152300-150000)/(2300))`

`=P(-1<Z<1)\\=0.68\\`

According to the 68-95-99.7, 68% of the data for a Normal distribution are within 1 standard deviations of the mean.

The correct option is D.

(14)

Compute the percentage of buyers who paid more than $154,800 as follows:

`P(X>154800)=P((X-\mu)/(\sigma)>(154800-150000)/(2400))`

`=P(Z>2)\\=0.975\\`

According to the 68-95-99.7, 95% of the data for a Normal distribution are within 2 standard deviations of the mean. Then the percentage of data above 2 standard deviations of the mean will be 97.5% and below 2 standard deviations of the mean will be 2.5%.

The correct option is D.

(15)

The z-score is given as follows:

`z=(x-\mu)/(\sigma)`