How many 3/4 are in 11/4

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

Inessa [10]

Answer:

73.3% probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 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 theore.

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 question, 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 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce

That is, probability of the sample mean between 8.2-0.02 = 8.18 and 8.2 + 0.02 = 8.22, which is the pvalue of Z when X = 8.22 subtracted by the pvalue of Z when X = 8.18.

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

73.3% probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100 jars, will be at most 0.02 ounce

6 0

3 years ago

A square tabletop has side lengths of (2x − 7) units. Enter a polynomial that represents the area of the tabletop.

abruzzese [7]

Answer:

53x-28x

Step-by-step explanation:

Area equals length tomes width, so multiply them. You would multiply them by using the distributive property, lastly add like terms.

5 0

3 years ago

Read 2 more answers

A poll shows that 50% of students play sports

Firlakuza [10]

Answer:

The chance of getting a sample proportion of 70% or greater is 0.026.

Step-by-step explanation:

We are given that a poll shows that 50% of students play sports .

A random sample of 20 students showed that 70% of them play sports.

Let $\hat p$ = sample proportion of students who play sports

The z-score probability distribution for the sample proportion is given by;

Z = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of students who play sports = 70%

p = population proportion of students who play sports = 50%

n = sample of students = 20

Now, the chance of getting a sample proportion of 70% or greater is given by = P( $\hat p$ $\geq$ 70%)

P( $\hat p$ $\geq$ 70%) = P( $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ $\geq$ $\frac{0.70-0.50}{\sqrt{\frac{0.70(1-0.70)}{20} } }$ ) = P(Z $\geq$ 1.95) = 1 - P(Z < 1.95)

= 1 - 0.97441 = <u>0.026</u>

The above probability is calculated by looking at the value of x = 1.95 in the z-table which has an area of 0.97441.

Hence, the chance of getting a sample proportion of 70% or greater is 0.026.

8 0

3 years ago

in the figure below,angle y and angle x from vertical angles.angle y forms a straight line with 80° angle and the 60° angle

nignag [31]

Can you add a picture?

5 0

3 years ago

Question 3

kirill115 [55]

B I believe if not sorry

3 0

3 years ago