Marquis used the steps below to find the solution to the inequality Negative 5.6 greater-than-or-equal-to x + 3.6.

In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hir

Georgia [21]

Answer:

a) the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204

b) the probability that the sample proportion will be within 0.04 of the population proportion is 0.95

c) sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061

d) the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088

e) gain in precision is 0.1402.

Step-by-step explanation:

a) Let p represent the

Given that

population proportion of complaints settled for new car dealers p = 0.75.

and n = 450

mean of the sampling distribution of the sample proportion is the population proportion p

i.e up° = p

mean of the sampling distribution of the sample proportion p° = 0.75

so standard error of the proportion is;

αp° = √(p( 1-p ) / n)

we substitute

αp° = √(0.75 ( 1-0.75 ) / 450)

=√(0.1875 / 450

= √0.0004166

= 0.0204

therefore the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204

b)

(p° - p) is within 0.04

so lets consider

p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 450)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 450))

= p( -0.04/0.0204 ≤ z ≤ 0.04/0.0204)

= p ( -1/96 ≤ z ≤ 1.96 )

= p( z < 1.96 ) - p( z < -1.96 )

now from the S-normal table,

area of the right of z = 1.96 = 0.9750

area of the left of z = - 1.96 = 0.0250

p( -0.04 ≤ p°- p ≤ 0.04) = p( z < 1.96 ) - p( z < -1.96 ) = 0.9750 - 0.0250

= 0.95

therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.95

c)

population proportion of complaints settled for new car dealers p = 0.75.

n = 200

mean of the sampling distribution of the sample proportion p°.

i.e up° = p

mean of the sampling distribution of the sample proportion p° = 0.75

Sampling distribution of the sample proportion p is determined as follows

αp° = √(p( 1-p ) / n)

we substitute

αp° = √(0.75 ( 1-0.75 ) / 200)

=√(0.1875 / 200

= √0.0009375

= 0.03061

therefore sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061

d)

(p° - p) is within 0.04

so lets consider

p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 200)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 200))

= p( -0.04/0.03061≤ z ≤ 0.04/0.03061)

= p ( -1.31 ≤ z ≤ 1.31 )

= p( z < 1.31 ) - p( z < -1.31 )

now from the S-normal table,

area of the right of z = 1.31 = 0.9049

area of the left of z = - 1.31 = 0.0951

p( -0.04 ≤ p°- p ≤ 0.04) = p( z < 1.31 ) - p( z < -1.31 ) = 0.9049 - 0.0951

= 0.8098

therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088

e)

From b), the sample proportion is within 0.04 of the population proportion; with the sample of 450 complaints involving new car dealers is 0.95.

sample proportion is within 0.04 of the population proportion; with the sample of 200 complaints involving new car dealers is 0.8098.

measured by the increase in probability, gain in precision occurs by taking the larger sample in part (b)

i.e

Gain in precision will be;

0.9500 − 0.8098

= 0.1402

therefore gain in precision is 0.1402.

8 0

2 years ago

The mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of

grandymaker [24]

Answer:

At the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Step-by-step explanation:

We are given that the mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000.

The ship building association wishes to find out whether their welders earn more or less than $20,000 annually.

Let $\mu$ = mean gross annual incomes of certified welders

So, Null Hypothesis, $H_0$ : $\mu$ = $20,000

Alternate hypothesis, $H_A$ : $\mu \neq$ $20,000

Here, null hypothesis states that the mean income of welders is equal to $20,000.

On the other hand, alternate hypothesis states that the mean income of welders is not $20,000.

Also, the test statistics that would be used here is One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean income

$\sigma$ = population standard deviation = $2,000

n = sample size

Now, at the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

3 0

2 years ago

The telephone company is planning to introduce two new types of executive communications systems that it hopes to sell to its la

cluponka [151]

Answer:

x = 31 hundred dolars and

y = 91/2 = 45.5 hundred dolars

Step-by-step explanation:

Given

R(x) = (40−8x+5y)*x + (50+9x−7y)*y

C(x) = (40−8x+5y)*10 + (50+9x−7y)*29

We can use the equation

P(x) = R(x) - C(x)

where

P(x) is the profit

R(x) is the revenue

and C(x) is the costs

In order to maximize the telephone company's profit, we apply

P'(x) = R(x)' - C(x)' = 0

⇒ R(x)' = ((40−8x+5y)*x + (50+9x−7y)*y)' = (40x-8x²+14xy+50y-7y²)'

⇒ C(x)' = ((40−8x+5y)*10 + (50+9x−7y)*29)' = (1850+181x-153y)'

⇒ P'(x) = -8x²-7y²-141x+203y+14xy-1850

The first-order partial derivatives of these functions are

Px(x,y) = -16x-141+14y

Py(x,y) = -14y+203+14x

Setting these equal to zero and solving we obtain:

-16x+14y-141 = 0

14x-14y+203=0

we get the solution

x = 31 and y = 91/2 = 45.5

Finally, the company should produce 3100 units of the first system, and 4550 units of the second system.

8 0

2 years ago

a homeowner plans to hang wallpaper on one wall of a bedroom that is 10 feet long. if a strip of wallpaper is 20 inches wide and

love history [14]

1 ft = 12 inches....so 10 ft = (10 * 12) = 120 inches

each strip of wall paper is 20 inches...

so 120/20 = 6 strips of wall paper are required <==

4 0

2 years ago

The equation |x − 8| = 3 represents the minimum and maximum percent of people in a survey who are undecided about an issue. What

icang [17]

| x - 8| = 3

x - 8 = 3 - (x - 8) = 3
x = 3 + 8 -x + 8 = 3
x = 11 -x = 3 - 8
-x = - 5
x = 5

Minimum : 5% Maximum : 11% if u need them added it is 16%

5 0

2 years ago

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