HELPPP PLEASE!!!!

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

Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 34 and, in a separa

Marina CMI [18]

<h3>The probability of winning the lottery is $\frac{1}{10,295,472}$ </h3>

Step-by-step explanation:

Here, the total numbers in the jackpot = 1 to 34

Now, the number that needed to be drawn = 5

The number of ways , 5 number can be drawn from total 34 numbers :

$^{34} C _5 = \frac{34!}{5!(34-5)!} = 278,256$

Also, in separate draw, the correct number drawn = 1

So, the number of ways that can be done = 30 C 5 x 37

= 278,256 x 37 = 10,295,472

Now, P(win) = $\frac{\textrm{Total favorable attempts}}{\textrm{Total attempts}} = \frac{1}{10,295,472}$

Hence, the probability of winning the lottery is $\frac{1}{10,295,472}$

6 0

3 years ago

A circle with a radius of 12 inches has an arc that measures 8 pi inches. Find the measure of the central angle determined by th

ivanzaharov [21]

We know that

[length of a circle]=2*pi*r
r=12 in
[length of a circle]=2*pi*12--------------> 24pi in

if 360° (full circle)--------------------> has a length of 24pi in
X-------------------------------------------> 8pi

X=8pi*360/24pi-----------> 120°

the answer is 120°

3 0

3 years ago

Mr. yates has an $80.00 budget to purchase a $72.00 pair of sunglasses. If there is a 6% sales tax rate, then how much under bud

Alekssandra [29.7K]

Answer:

$3.68 underbudget

Step-by-step explanation:

$72*6%\\72*0.06=4.32\\Tax=4.32\\72+4.32=76.32 \ Total\\80-76.32=3.68$

Hope this helped!

6 0

3 years ago

A company has 2 photocopy machines. The probability that machine A will breakdown on a given day is 2%. The probability that mac

pickupchik [31]

Answer: 95.55%

--------------------------------

Work Shown:

A = event that copier A breaks down
B = event that copier B breaks down

P(A) = probability that copier A breaks down
P(A) = 2% = 0.02

P(B) = probability that copier B breaks down
P(B) = 2.5% = 0.025

P(neither break down) = (1-P(A))*(1-P(B))
P(neither break down) = (1-0.02)*(1-0.025)
P(neither break down) = 0.9555
P(neither break down) = 95.55%

8 0

3 years ago

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