Can someone please help me with this:)

andrezito [222]

Answer:

a) 0.27% probability that the mean is less than 1995 milliliters.

b) 2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

Step-by-step explanation:

To solve this problem, it is important 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:

$\mu = 2000, \sigma = 18$

A) If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1995 milliliters?

So $n = 100, s = \frac{18}{\sqrt{100}} = 1.8$

This probability is the pvalue of Z when X = 1995. So

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

By the Central Limit Theorem

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

$Z = \frac{1995 - 2000}{1.8}$

$Z = -2.78$

$Z = -2.78$ has a pvalue of 0.0027

So 0.27% probability that the mean is less than 1995 milliliters.

B) What mean overfill or more will occur only 10% of the time for the sample of 100 bottles?

This is the value of X when Z has a pvalue of 1-0.1 = 0.9.

So it is X when $Z = 1.28$

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

$1.28 = \frac{X - 2000}{1.8}$

$X - 2000 = 1.8*1.28$

$X = 2002.3$

2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

3 0

3 years ago

Marta exercises 30 minutes each day Greg exercises 40 minutes a each day how many more minutes does Greg exercise than Marta in

ryzh [129]

40-30=10 minutes more per day x 31 days = 310minutes in a month with 31 days.

6 0

3 years ago

Read 2 more answers

PLEASE HELP!

butalik [34]

We know for the problem that the performer earned $120 at a performance where 8 people attend. We also know that he uses 43% of the money earned to pay the costs involved in putting on each performance, so we need to find the 43% of $120. To do that, we are going to divide 43% by 100%, and then multiply it by $120:
 $\frac{43}{100}*120=51.6$
Now we know that the performer uses $51.6 of $120 to pay the costs involved in putting on each performance. The only thing left to find his profits is subtract $51.6 from $120:
$120-51.6=68.4$

We can conclude that the performer makes a profit of $68.4 when 8 people attend his performance.

3 0

3 years ago

A right triangle has side lengths d, e, and f as shown below.

DIA [1.3K]

Answer:

and f as shown below.

Use these lengths to find cosx, sinx, and tanx.

Step-by-step explanation:

5 0

3 years ago

Max was on vacation twice as long is Jared and half as long as Wesley. The boys were on vacation a total of three weeks. How man

nasty-shy [4]

To begin with, the question is asking for the answer in days, so let's change 3 weeks to days. There are 7 days in 1 week; 3 weeks times 7 days = 21 days.
21 total days of vacation.

Max + Jared + Wesley = 21 days
(Let's use the first letter of their name to represent their vacation time)

M + J + W = 21 [This is the equation we'll be coming back to]

Now, we can use the clues given in the question to have an equation for each variable/boy.

Max was on vacation twice as long as Jared. We can interpret this as M= 2J Max was on vacation only half as long as Wesley. We can interpret this as M = (1/2)W.

So far we have these three equations: M + J + W = 21M = 2J M = (1/2)W

To have an equation for each individual boy, we must rearrange the last two equations in the list.

First, M = 2J.
Divide both sides by 2
M/2 = 2J/2
(1/2)M = J

Second, M = (1/2)W
Multiply both sides by 2
2M = W

New equations:
M + J + W = 21 [From the old list]
J = (1/2)W
W = 2M

Now we can substitute the last two equations into the first one.
M + J + W = 21
M + (1/2)W + 2M = 21
[Combine Like Terms]
(7/2)M = 21

Then, solve for M (Max's vacation days):
Multiply both sides by 2/7
$(\frac{2}{7})* (\frac{7}{2}m)= (\frac{2}{7})*(21)$
M = 6

Now we know Max was on vacation for 6 days.

If Max was on vacation twice as long as Jared, that means Jared was on vacation HALF as long as Max.

So...
J = (1/2)M
J = (1/2) * 6
J = 3
Jared was on vacation for 3 days

Wesley was on vacation twice as long as Max so... W = 2M
W= 2*6
W = 12
Wesley was on vacation for 12 days.

Let's double check our answer:
M + J + W = 21 days6 + 3 + 12 = 21
The numbers work out so the math is correct. Hope this helps and makes sense!

6 0

3 years ago

Can someone please help me with this:) ​

Can someone please help me with this:)