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Maddy and her cousin work during the summer for a landscaping company. Maddy's cousin has been working for the company longer, s

anygoal [31]

Hope it helps u mate. Plz follow me :)

8 0

3 years ago

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

2 years ago

Round 491,778 to the nearest hundred

hichkok12 [17]

Answer:

491,800!

Step-by-step explanation:

6 0

3 years ago

Identify the parameters in y = a*bkx.

Natasha2012 [34]

Convention in algebra is that we use letters such as a, b, c, etc., for parameters and letters such as x, y z, and so on, for variables.

Thus the parameters here are a, b and k. k is the constant of proportionality.

5 0

3 years ago

Jake and Danny agree to share the cost of renting a house for $1100. If Jake agrees to pay $250 more than Danny, how much money

SVEN [57.7K]

Step-by-step explanation:

First divide 1100 by 2

550

Now that would be the amount the both of them would have to pay if they were splitting it equally. Since there not add 250 to 550.

250+550=800

Finally subtract 250 from 550

550-250=300

Jake has to pay $550

Danny has to pay $300

7 0

3 years ago