What is midpoint 85 90?

two of the interior angles of a polygon are 134° and 156° and each of the remaining angles is 151°. find no of sides of the poly

muminat

the side of a polygon is 12 side polygon

8 0

3 years ago

19. A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years

Juliette [100K]

Answer:

a) Approximately normal.

b) The mean is 75 years and the standard deviation is 0.8485 years.

c) 0.9909 = 99.09% probability that the mean age exceeds 73 years

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Sample of 50 retirees

This means that $n = 50$

Mean age and standard deviation are 75 and 6 years

This means that $\mu = 75, \sigma = 6$

a. Describe the shape of the sampling distribution of the sample mean in this case

By the Central Limit Theorem, approximately normal.

b. Find the mean and standard error of the sampling distribution of the sample mean.

By the Central Limit Theorem, the mean is 75 and the standard error is $s = \frac{6}{\sqrt{50}} = 0.8485$

c. What is the probability that the mean age exceeds 73 years?

This is 1 subtracted by the pvalue of Z when X = 73.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{73 - 75}{0.8485}$

$Z = -2.36$

$Z = -2.36$ has a pvalue of 0.0091

1 - 0.0091 = 0.9909

0.9909 = 99.09% probability that the mean age exceeds 73 years

5 0

3 years ago

What is an equation of the horizontal asymptote or slant asymptote of the function f(x)=−8x2 + 54x − 474x − 5?

RSB [31]

Answer:

89

Step-by-step explanation:

I took the same exact test 9

8 0

3 years ago

∠1 and ∠2 are vertical angles. ∠2 has a measure of 31°. What is the measure of ∠1 ? Enter your answer in the box. °

Nesterboy [21]

The meaning of vertical angles are two congruent angles formed by the intersection of two straight lines.

On this question is given that angles one and two are vertical, and the measure of one of them or angle two is 31 degrees.
As said before vertical angles are congruent, or have the same measurement.

Meaning that angle one is equal to 31 degrees.

8 0

3 years ago

Read 2 more answers

What is the equation of a line that passes through the points (3, 6) and (8, 4) in slope intercept form?

MrMuchimi

Answer:

$y=-\frac{2}{5}x +8.4$