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The mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50 with a standard deviation of $5.00. Assum

DochEvi [55]

Answer:

a. $\mathtt{P(X \geq 25) =0.0170}$ ( to four decimal places)

b. $P(22.5$ ( to four decimal places )

c. The limits will be between the interval of ( 22.33,24.67 )

Step-by-step explanation:

Given that :

mean = 23.50

standard deviation = 5.00

sample size = 50

The objective is to calculate the following:

(a) What is the likelihood the sample mean is at least $25.00?

Let X be the random variable, the probability that the sample mean is at least 25.00 is:

$P(X \geq 25) = 1 - P(\dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{25- 23.50}{ \dfrac{5}{\sqrt{ 50}} })$

$P(X \geq 25) = 1 - P(Z< \dfrac{1.5}{ \dfrac{5}{7.07107}} })$

$P(X \geq 25) = 1 - P(Z< \dfrac{1.5 \times 7.071}{ {5}})$

$P(X \geq 25) = 1 - P(Z< 2.1213)$

$P(X \geq 25) = 1 - P(Z< 2.12)$ to two decimal places

From the normal tables :

$P(X \geq 25) = 1 - 0.9830$

$\mathtt{P(X \geq 25) =0.0170}$ ( to four decimal places)

(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00?

$P(22.5$

$P(22.5$ to four decimal places

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

At 90 % confidence interval, level of significance = 1 - 0.90 = 0.10

The critical value for the $z_{\alpha/2} = 0.05$ = 1.65

Standard Error = $\dfrac{\sigma}{\sqrt{n}}$

Standard Error = $\dfrac{5}{\sqrt{50}}$

Standard Error = 0.7071

Therefore, at 90 percent of the sample means, the limits will be between the intervals of : $(\mu \pm z_{\alpha/2} \times S.E)$

Lower limit = ( 23.5 - (1.65×0.707) )

Lower limit = ( 23.5 - 1.16655 )

Lower limit = 22.33345

Lower limit = 22.33 (to two decimal places).

Upper Limit = ( 23.5 + (1.65*0.707) )

Upper Limit = ( 23.5 + 1.16655 )

Upper Limit = 24.66655

Upper Limit = 24.67

The limits will be between the interval of ( 22.33,24.67 )

6 0

3 years ago

Which of the following is TRUE about the hypotenuse?

svetoff [14.1K]

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2 years ago

What is the equation of the line in slope-intercept form?

Mekhanik [1.2K]

Answer:

It's the second option -> y = 1/2x -1

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3 years ago

The slope of the line below is 1 .write the point slope equation for the line using the coordinates of the labeled point. (5,7)

wariber [46]

Answer:

Step-by-step explanation:

The point slope equation of a line is expressed as;

y - y0 = m(x-x0)

m is the slope

(x0, y0) is the point on the line

Given the following

m = 1

(x0, y0) = (5, 7)

Substitute into the formula

y - 7 = 1 (x - 5)

y - 7 = x -5

y = x - 5 + 7

y = x + 2

<em>Hence the point slope equation of the line is y - 7 = 1 (x-5)</em>

3 0

2 years ago

The cost of 1 m ribbon is ₹ 75. Find the cost of 7/5 metres of ribbon

Margaret [11]

Given that

The cost of 1 m ribbon = Rs.75

The cost of 7/5 m ribbon

→ (7/5)×75

→ (7×75)/5

→7×15

→₹ 105

The cost of 7/5 m ribbon is ₹105.

8 0

3 years ago