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3 years ago

The task I need explaining is: how to show that an estimate of the mean time spent on homework is 64.8 minutes. Thanks!

Mathematics

1 answer:

xenn [34]3 years ago

5 0

It's just an estimate. There's no telling how close it is.

To estimate using just the information in the table,
ASSUME that the average of all the students in each
slot is the average time of that slot.

I know that's confusing. I can't think of a better way to say it,
so here are two examples of what I mean. Look at the table:

-- 6 students said that they spent between 0 and 30 minutes.
ASSUME that those 6 students averaged 15 minutes each.

-- 21 students said that they spent between 60 and 90 minutes.
ASSUME that those 21 students averaged 75 minutes each.

So, when you add up the times for all 50 students, you'll have

(6 x 15 min) + (14 x 45 min) + (21 x 75min) + (9 x 105 min) =

When you total up all those times, divide it by 50 to estimate
the average per student.

Remember ... it's only an estimate.
If the first group had 1 student that spent 2 minutes, and
the other 5 of them spent 29 minutes, then it won't work.
But you'll never know.

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. Exam scores for a large introductory statistics class follow an approximate normal distribution with an average score of 56 an

Andru [333]

Answer:

0.1% probability that the average score of a random sample of 20 students exceeds 59.5.

Step-by-step explanation:

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 $\frac{\sigma}{\sqrt{n}}$

Normal probability distribution

Problems of normally distributed samples can be 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.

In this problem, we have that:

$\mu = 56, \sigma = 5, n = 20, s = \frac{5}{\sqrt{20}} = 1.12$

What is the probability that the average score of a random sample of 20 students exceeds 59.5?

This is 1 subtracted by the pvalue of Z when $X = 59.5$ . So

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

$Z = \frac{59.5 - 56}{1.12}$

$Z = 3.1$

$Z = 3.1$ has a pvalue of 0.9990.

So there is a 1-0.9990 = 0.001 = 0.1% probability that the average score of a random sample of 20 students exceeds 59.5.

3 0

3 years ago

What is the slope of the line that passes through the pair of points (-2.5,6.1) and (-2.5,3.1)

podryga [215]

(-2.5,6.1)(-2.5,3.1).....notice how ur x values are the same. This means that u have a vertical line which has an undefined slope.

IF ur y values would have been the same, u would have had a horizontal line which has a 0 slope.

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3 years ago

How do you solve 5x-2y= 18 and -5x+3y= -22 by solving a system of linear equations by elimination? Please add the steps in which

MaRussiya [10]

Write the 2 equations:

5x-2y=18
-5x+3y=-22

You can see that the coefficients of x are opposites, so you can add them(the 2 equations) to eliminate x.

Adding them, you get:

y=-3

So now that you know y, you can substitute the value of y into one of the original equations. Let's substitute it in the first one:

5x+6=18

Solving this, we get:

5x=12
x=12/5

x=12/5, y=-3

3 0

3 years ago