Question

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

Answer 1

Answer:

Explained below.

Step-by-step explanation:

(10)

The data set is:

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

The mean and standard deviation are:

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

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

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

$X=\mu-2\sigma$

    $=100-(2\times 26)\\=100-52\\=48$

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:

$P(147700$

                                         $=P(-1$                                        

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:

$P(X>154800)=P(\frac{X-\mu}{\sigma}>\frac{154800-150000}{2400})$

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

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:

$z=\frac{x-\mu}{\sigma}$