What 0.04 percent form is?

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

An animal shelter has a 58% adoption rate for puppies. Of all puppies in the shelter, 80% live to be 7 years or older. Of the pu

dexar [7]

Answer:

P(A∩B) = 0.522

Step-by-step explanation:

Let's call A the event that a puppy is adopted and B the probability that a puppy live 7 or more years

So, the probability P(A∩B) that a randomly selected puppy in the shelter will get adopted and live 7 or more years is:

P(A∩B) = P(A)*P(B/A)

Because A and B are not independents.

Then, the probability P(A) that a puppy is adopted is 58% and the probability P(B/A) that a puppy live 7 or more years given that the puppy is adopted is 90%.

Finally, replacing the values, we get:

P(A∩B) = 0.58*0.9 = 0.522

It means that the 52.2% of the puppies are adopted and live 7 or more years.

7 0

3 years ago

Solve for n nn. 7 n − 4 = 31

makkiz [27]

Answer: 5

Step-by-step explanation:

5x7=35

35-4=31

5 0