5(x 1) − 8 = 5x(2 − 4)

A half-century ago, the mean height of women in a particular country in their 20s was 64.7 inches. Assume that the heights of

Ainat [17]

Answer:

99.5% of all samples of 21 of today's women in their 20's have mean heights of at least 65.86 inches.

Step-by-step explanation:

We are given that a half-century ago, the mean height of women in a particular country in their 20's was 64.7 inches. Assume that the heights of today's women in their 20's are approximately normally distributed with a standard deviation of 2.07 inches.

Also, a samples of 21 of today's women in their 20's have been taken.

Let $\bar X$ = sample mean heights

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean height of women = 64.7 inches

$\sigma$ = standard deviation = 2.07 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the sample of 21 of today's women in their 20's have mean heights of at least 65.86 inches is given by = P( $\bar X$ $\geq$ 65.86 inches)

P( $\bar X$ $\geq$ 65.86 inches) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ $\geq$ $\frac{65.86-64.7}{\frac{2.07}{\sqrt{21} } }$ ) = P(Z $\geq$ -2.57) = P(Z $\leq$ 2.57)

= 0.99492 or 99.5%

The above probability is calculated by looking at the value of x = 2.57 in the z table which has an area of 0.99492.

Therefore, 99.5% of all samples of 21 of today's women in their 20's have mean heights of at least 65.86 inches.

3 0

3 years ago

Four times the larger of two consecutive even integers is ten less than the smaller. What is the larger of these two numbers?

anygoal [31]

Answer:

-4 is the larger integer

Step-by-step explanation:

n = smaller integer

n + 2 = larger integer

4(n+2) = n-10

4n + 8 = n - 10

3n + 8 = -10

3n = -18

n = -6

n+2 = -4

7 0

3 years ago

Find the future sum of a present value of $2,000 deposited in a bank at 5% interested for 8 years, compounded continuously (F=Pe

tatiyna

Answer:

$2983.65

Step-by-step explanation:

A = $2000 $e^{8*.05}$ =

3 0

3 years ago

Determine if the linear system

zubka84 [21]

Answer:

b. The system is not in echelon form because the system is not organized in descending "stair step" pattern so that the index of the leading variables increases from the top to bottom.

Step-by-step explanation:

The given linear system has a equation which is not in echelon form. The echelon is a system which divides the data into rigid hierarchal groups. The given linear equation in not in echelon form as the leading variables are increased from top to bottom indicating descending stair step pattern.

4 0

3 years ago

The measure of angle J is 120⁰ and is vertical to the measure of angle K. If the measure of angle K is x , what is the value of

Gnoma [55]

Answer:

x=120

Step-by-step explanation:

a vertical angle is equal to each other so if angle J is 120° the so is angle K

4 0

3 years ago