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Taya2010 [7]
3 years ago
10

Find the y-intercept of the parabola whose equation is f(x)=-2x^2-8x+5

Mathematics
1 answer:
tatyana61 [14]3 years ago
6 0

Answer:

i'm pretty sure the y-intercept would be 5

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The mean amount purchased by a typical customer at Churchill's Grocery Store is $27.50 with a standard deviation of $7.00. Assum
Schach [20]

Answer:

a) 0.0016 = 0.16% probability that the sample mean is at least $30.00.

b) 0.8794 = 87.94% probability that the sample mean is greater than $26.50 but less than $30.00

c) 90% of sample means will occur between $26.1 and $28.9.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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 = 27.50, \sigma = 7, n = 68, s = \frac{7}{\sqrt{68}} = 0.85

a. What is the likelihood the sample mean is at least $30.00?

This is 1 subtracted by the pvalue of Z when X = 30. So

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

By the Central Limit Theorem, we have that:

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

Z = \frac{30 - 27.5}{0.85}

Z = 2.94

Z = 2.94 has a pvalue of 0.9984

1 - 0.9984 = 0.0016

0.0016 = 0.16% probability that the sample mean is at least $30.00.

b. What is the likelihood the sample mean is greater than $26.50 but less than $30.00?

This is the pvalue of Z when X = 30 subtracted by the pvalue of Z when X = 26.50. So

From a, when X = 30, Z has a pvalue of 0.9984

When X = 26.5

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

Z = \frac{26.5 - 27.5}{0.85}

Z = -1.18

Z = -1.18 has a pvalue of 0.1190

0.9984 - 0.1190 = 0.8794

0.8794 = 87.94% probability that the sample mean is greater than $26.50 but less than $30.00.

c. Within what limits will 90 percent of the sample means occur?

Between the 50 - (90/2) = 5th percentile and the 50 + (90/2) = 95th percentile, that is, Z between -1.645 and Z = 1.645

Lower bound:

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

-1.645 = \frac{X - 27.5}{0.85}

X - 27.5 = -1.645*0.85

X = 26.1

Upper Bound:

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

1.645 = \frac{X - 27.5}{0.85}

X - 27.5 = 1.645*0.85

X = 28.9

90% of sample means will occur between $26.1 and $28.9.

4 0
2 years ago
Jana earns $25 per week for mowing the lawn and deposits the money into her savings account. The amount of money in Jana’s accou
photoshop1234 [79]

Slope-intercept form: y = mx + b  [m is the slope, b is the y-intercept or the y value when x = 0  --->  (0, y)  or the point where the line crosses through the y-axis]

y = 25x + 125

"y" would represent the total amount of $ she has saved.

The y-intercept would be 125 or (0, 125), this means that she already/initially had $125 in her savings account, before she started depositing $25 per week

7 0
3 years ago
Use the relationships between the angles to find the value of x (please answer)
Varvara68 [4.7K]

Step-by-step explanation:

x + 15 \degree = 102 \degree \:  \\ (corresponding \:  \angle s) \\  \therefore \: x =  102 \degree -  15 \degree  \\  \huge \red { \boxed{\therefore \: x =  87 \degree}}

4 0
3 years ago
A school supply store owner sold 9 book bags and earned $270.00
mamaluj [8]
The answer to this is D, $990.00
4 0
3 years ago
CAN SOMEONE JUST CHECK MY ANSWER?
12345 [234]

Answer:

you are absolutely correct .........

6 0
2 years ago
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