Is the solution of a system of linear inequalities the union or intersection of the splutions of the two inequalities?

Assume the average height for American women is 64 inches with a standard deviation of 2 inches. A sorority on campus wonders if

satela [25.4K]

Answer:

a) s = 0.4

b) Z = 2.5

c) 99th percentile.

d) The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

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 establishes 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.

Assume the average height for American women is 64 inches with a standard deviation of 2 inches

This means that $\mu = 64, \sigma = 2$

A) Calculate the standard error for the distribution of means.

Sample of 25 means that $n = 25$ , so $s = \frac{2}{\sqrt{25}} = 0.4$ .

B) Calculate the z statistic for the sorority group.

Sample mean of 65 means that $X = 65$ .

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{0.4}$

$Z = \frac{65 - 64}{0.4}$

$Z = 2.5$

C) What is the approximate percentile for this sample? Enter as a whole number.

Z = 2.5 has a p-value of 0.9938, so 0.99*100 = 99th percentile.

D) If the sorority actually had 36 members (still with an average of 65 inches), would you expect the percentile value to increase or decrease? why?

The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

3 0

3 years ago

A college Statistics class conducted a survey concerning community attitudes about the college's large homecoming celebration. T

gogolik [260]

Answer:

A) Yes

B) No

C) No

D) No

Step-by-step explanation:

A) Yes, every telephone number that could occur in that community will have an equal chance of being generated because the telephone numbers were generated randomly.

B) No, this method of generating telephone numbers would not result in a simple random sample (SRS) of local residences because the first three digits were generated in a different random way than the last four digits.

C) No, this method would not generate an SRS of local voters because not everybody will be pick up when they call because they may not be at home or they may be too busy to pick up.

D) No, this method is not unbiased in generating samples of households because there will be nonresponse bias since not everyone will pick up the call

4 0

3 years ago

What is the best estimate of 42% of 756? a)320 b)240 c)400 d)400

nataly862011 [7]

320 i believe... the original answer was 317.52

4 0

3 years ago

Read 2 more answers

P (-2,6), Q (9,6), R (7, -1), S (-4, -1) are the vertices of a quadrilateral.

vova2212 [387]

Step-by-step explanation:

Parallelogram

Reflect y=-1 ;x changes sign

6 0

3 years ago

An electronic product contains 48 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the

BigorU [14]

Answer:

0.6173 = 61.73% probability that the product operates.

Step-by-step explanation:

For each integrated circuit, there are only two possible outcomes. Either they are defective, or they are not. The integrated circuits are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$