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Vesnalui [34]
3 years ago
11

Use substitution to solve the system of equations.

Mathematics
1 answer:
never [62]3 years ago
8 0
Subtract the Y from the x and the x from the y that is how you would get the answer this is how you would find slope
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The mean amount purchased by a typical customer at Churchill's Grocery Store is $26.00 with a standard deviation of $6.00. Assum
Vadim26 [7]

Answer:

a) 0.0951

b) 0.8098

c) Between $24.75 and $27.25.

Step-by-step explanation:

To solve this question, we need 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 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 problem, we have that:

\mu = 26, \sigma = 6, n = 62, s = \frac{6}{\sqrt{62}} = 0.762

(a)

What is the likelihood the sample mean is at least $27.00?

This is 1 subtracted by the pvalue of Z when X = 27. So

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

By the Central Limit Theorem

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

Z = \frac{27 - 26}{0.762}

Z = 1.31

Z = 1.31 has a pvalue of 0.9049

1 - 0.9049 = 0.0951

(b)

What is the likelihood the sample mean is greater than $25.00 but less than $27.00?

This is the pvalue of Z when X = 27 subtracted by the pvalue of Z when X = 25. So

X = 27

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

Z = \frac{27 - 26}{0.762}

Z = 1.31

Z = 1.31 has a pvalue of 0.9049

X = 25

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

Z = \frac{25 - 26}{0.762}

Z = -1.31

Z = -1.31 has a pvalue of 0.0951

0.9049 - 0.0951 = 0.8098

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

50 - 90/2 = 5

50 + 90/2 = 95

Between the 5th and the 95th percentile.

5th percentile

X when Z has a pvalue of 0.05. So X when Z = -1.645

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

-1.645 = \frac{X - 26}{0.762}

X - 26 = -1.645*0.762

X = 24.75

95th percentile

X when Z has a pvalue of 0.95. So X when Z = 1.645

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

1.645 = \frac{X - 26}{0.762}

X - 26 = 1.645*0.762

X = 27.25

Between $24.75 and $27.25.

3 0
3 years ago
Please help me with this, I'm timed right now and the assignment is due today soooooooo........ Please help. Ok, now to the ques
Ipatiy [6.2K]

The total number of people in the city surveyed by Annette= 480 people.

Step-by-step explanation:

Let 'X' be the Total Number of people Annette surveyed.

Out of Total people in the city, only <u>180 people are not interested</u> in a new shopping mall.

Therefore, it is given in the question that <u>180 is 37.5% of Total number of people surveyed (X).</u>

step 1: 180= (37.5/100)*(X)

step 2: X= (180*100)/37.5

step 3: X= 18000/37.5

step 4: X= 480

4 0
3 years ago
Convert the given amount to the given unit.<br> 6.5 lb; ounces<br> 6.5 lb =<br> ounces
Aneli [31]

Answer:

the answer is 104

Step-by-step explanation:

1= 16

6= 96

0,5=8

5 0
3 years ago
What equation could be used to determine 23% of 122?​
ArbitrLikvidat [17]

First, convert 23% into a fraction.

23% =

23 \div 100 =  \frac{23}{100}

Now the expression to determine 23% of 122 is

\frac{23}{100}  \times 122 \\  = ( \frac{23}{100} )(122)

7 0
3 years ago
Read 2 more answers
3. The sum of two numbers is 17. The difference between the larger number and the
Leno4ka [110]

Answer:

5

Step-by-step explanation:

To solve this problem, we need to set up a system of equations. Let x represent the larger number and y represent the smaller number.

x + y = 17

x - y = 7

We can solve this system by adding them together. The y cancels out because y + (-y) = 0. After that, we solve for x

2x = 24          

x = 12              (Divide both sides by 2)

Now that we know the value of x, we can substitute it into one of our original equations to solve for y.

12 + y = 17      

y = 5                (Subtract 12 from both sides)

So, the smaller number is 5.

4 0
2 years ago
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