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lesantik [10]
3 years ago
10

3) 6 cm 5 cm I 7 cm 5 cm 6 cm

Mathematics
1 answer:
lord [1]3 years ago
6 0

Answer:

29

Step-by-step explanation:

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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
How to find the average rate of change of a function
ollegr [7]

ANSWER

Average Rate of Change

=  \frac{f(b) - f(a)}{b - a}

EXPLANATION

To find the average rate of change of y=f(x) from x=a to x=b means finding the slope of the secant line joining the points

(a,f(a)) and (b,f(b))

The slope of the secant line joining these points is

=  \frac{f(b) - f(a)}{b - a}

This gives the average rate of change of the function.

5 0
3 years ago
Help on Number 8? I know Y=5 and the slope is undefined and x=2 but I don’t know what to do now.
Stels [109]

To find the slope, use the equation of a line: y = mx + b

Plug in the values for x and y:

5 = 2x + b

We know that 2 can fit into 5 twice, which means 2*2 is 4.

We now have 5 = 4 + b.

If 5 is b more than 4, then this means that 4 is b less than 5. Subtract 4 from both sides, and you will have b = 1.

This means your equation is y = 2x + 1.

3 0
3 years ago
Type an equation for the line shown in the graph
natulia [17]
0x+2 =y
So technically x+2=y
4 0
3 years ago
A company has $54,000 in a bank account that pays an interest of 2% per year. How much money can I withdraw at the end of one ye
RSB [31]

Answer:

$55,080

Step-by-step explanation:

Hope this helps.

3 0
3 years ago
Read 2 more answers
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