Computer monitors are measured by length of the screens what is the save of the tv is the sides ar 38 and 28.5

The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta

nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

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 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.

In this problem, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

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

By the Central Limit Theorem

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

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

X = 8.18

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

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0

3 years ago

in a standard deck of t2 playing cards, there are 4 aces, 4 kings, 4 queens, and 4 Jacks. All other cards have number values. th

Illusion [34]

Answer:

0.01

Step-by-step explanation:

Assuming the deck is the national playing deck with 52 cards.

Your probability of getting a 3 from the entire deck is 4/52. This number is the same for 10.

To get the probability of pulling a 3 and a 10 afterwards, you must multiply these two fractions (you're expecting a lower percentage).

$4/52 * 4/52 = 0.0059$

3 0

3 years ago

Two computers working together can finish a search in 30 seconds. One of these computers can finish in 50 seconds. How long woul

vivado [14]

It would take the second computer 75 seconds because:

$\frac{1}{30} - \frac{1}{50} = \frac{1}{75}$

6 0

3 years ago

If each face on a standard die shows a number,1,2,3,4, 5 or 6.If the die is tossed 30 times, how many times would you expect to

Vikki [24]

Answer:

We should get a 3 about 5 times

Step-by-step explanation:

Possible outcomes 1,2,3,4,5,6

P(3) = number of 3's / total = 1/6

Expect a 3 = number of rolls * probability of a three

= 30 * 1/6

=5

4 0

3 years ago

Helpp plsss right now

asambeis [7]

Answer:

<DEF = 107

Step-by-step explanation:

The way to best solve this problem is by starting with angle F. Remember that all angles in a straight line must add up to 180. So by subtracting 135 from 180 we get 45 for angle F.

180 - 135 = 45

After that, we can figure out the measure of <DEF. All the angles of a triangle must add up to 180. So:

180 - 28 - 45 = 107

Making the answer 107 for the measure of <DEF

3 0

2 years ago