Mathematics, 02.03.2020 20:48 daydallas01

Achievement test scores from all high-school seniors in a certain state have a mean and variance of 60 and 64, respectively. A specific high school class of n=100 students had a mean score of 58. Is there evidence to suggest that this high school is substandard? (Consider calculating the probability that the sample mean is at most 58 when n=100)

Answers: 2

Show answers

Answers

Answer from: fbpsye69

0.62% that the sample mean is at most 58. Any probability lower than 5% is considered unusually low, which means that there is evidence to suggest that this high school is substandard.

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 normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

Also important to remember that the standard deviation is the square root of the variance. So

$\mu = 60, \sigma = sqrt{64} = 8, n = 100, s = \frac{8}{\sqrt{100}} = 0.8$

A specific high school class of n=100 students had a mean score of 58. Is there evidence to suggest that this high school is substandard? (Consider calculating the probability that the sample mean is at most 58 when n=100)

This probability is the pvalue of Z when X = 58. So

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

By the Central Limit Theorem

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

$Z = \frac{58 - 60}{0.8}$

Z = -2.5

Z = -2.5 has a pvalue of 0.0062.

So there is a 0.62% that the sample mean is at most 58. Any probability lower than 5% is considered unusually low, which means that there is evidence to suggest that this high school is substandard.

Answer from: Quest

Gggģcawrygr3ezt9d hu and the other countries have been working to make it easier to box up their homes in an area where the government has not yet decided which countries will have the option of the government

Answer from: Quest

sadsadsadsad

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 16:50

The vertices of a triangle are a(7,5), b(4,2), c(9,2). what is m

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

Twenty points. suppose that one doll house uses the 1 inch scale, meaning that 1 inch on the doll house corresponds to 1/2 foot for life-sized objects. if the doll house is 108 inches wide, what is the width of the full-sized house that it's modeled after? in inches and feet

Answers: 2

Answer

Mathematics, 21.06.2019 19:50

If the scale factor between two circles is 2x/5y what is the ratio of their areas?

Answers: 3

Answer

Mathematics, 21.06.2019 20:00

The two cylinders are similar. if the ratio of their surface areas is 9/1.44 find the volume of each cylinder. round your answer to the nearest hundredth. a. small cylinder: 152.00 m3 large cylinder: 950.02 m3 b. small cylinder: 972.14 m3 large cylinder: 12,924.24 m3 c. small cylinder: 851.22 m3 large cylinder: 13,300.25 m3 d. small cylinder: 682.95 m3 large cylinder: 13,539.68 m3

Answers: 2

Answer

You know the right answer?

Achievement test scores from all high-school seniors in a certain state have a mean and variance of...

Questions