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Eduardwww [97]
2 years ago
3

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is d

etermined to be 600. At 95% confidence, the margin of error is
Mathematics
1 answer:
aleksley [76]2 years ago
5 0

Answer:

Margin of error is 9.8

Step-by-step explanation:

Using the formular for the margin of error

The margin of error = z* (sd/√n)

Where z is the z score for the desired confidence level = 1.96, sd is the population standard deviation = 50 and n is the sample size = 100

Thus

Margin of error = 1.96 (50/√100)

= 1.96 (50/10)

= 1.96 (5)

= 9.8

Margin of error is 9.8

You might be interested in
What is the solution to the inequality 2 + 4/9x _> 4 + x
Vsevolod [243]
Multiply each side by 9:
18 + 4x > 36 + 9x
Subtract 18 from each side:
4x > 18 + 9x
Subtract 9x from each side:
-5x > 18
Divide each side by -5:
x < -3.6

Hope this helps!

8 0
2 years ago
A carpool service has 2,000 daily riders. A one-way ticket costs $5.00. The service estimates that for each $1.00 increase to th
solmaris [256]

Answer:

Total number of riders that ride on carpool daily = 2000

Total Cost of one way ticket = $ 5.00

Total Amount earned if 2000 passengers rides daily on carpool = 2000 × 5

                                                                                                            = $10,000

If fare increases by $ 1.00

New fare = $5 + $1    

               = $6

Number of passengers riding on carpool = 2,000 - 100 = 1,900

If 1,900 passengers rides on carpool daily , total amount earned ,if cost of each ticket is $ 6 = 1900 × $6 = $11400

As we have to find the inequality which represents the values of x that would allow the carpool service to have revenue of at least $12,000.

For $ 1 increase in fare = (2,000 - 1 × 100) passengers

For $ x increase in fare, number of passengers = 2,000 - 100·x

                                                         = (2,000 - 100·x) passengers

New fare = 5 + x

New Fare × Final Number of passengers ≥ 12,000

(5+x)·(2,000 - 100 x) ≥ 12,000

5 (2,000 - 100 x) + x(2,000 - 100 x) ≥ 12,000

10,000 - 500 x + 2,000 x - 100 x² ≥ 12,000

100 - 5 x + 20 x - x² ≥ 120

- x² + 15 x +100 - 120 ≥ 0

-x² + 15 x -20 ≥ 0

x² - 15 x + 20 ≤ 0

⇒ x = 1.495

x ≥ $ 1.495, that is if we increase the fare by this amount or more than this the revenue will be at least 12,000 or more .

Also, f'(x) = 0 gives x = 7.5

⇒ The price of a one-way ticket that will maximize revenue is $7.50

7 0
2 years ago
A collection of 108 coins containing only quarters and nickels is worth $21. A table titled Coin Collection showing Number of Co
harina [27]

Answer:

q = 108-n

Step-by-step explanation:

Given: 108 coins containing only quarters and nickels

q = 108-n

since total number of coins is 108, and n= number of nickels

If you want to know how many of each kind of coin, read on:

First solve the number of quarters and nickels.

If all 108 coins are quarters, the value is 108*0.25 = $27

Since this value exceed the actual by 27-21 = $6,

we replace a number of quarters by nickels.

Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.

So it will take 6/0.2 = 30 replacements.

Therefore there are 108-35 = 78 quarters and 30 nickels.

8 0
2 years ago
Read 2 more answers
In 1990, the mean duration of long-distance telephone calls originating in one town was 7.2 minutes. A long-distance telephone c
scoundrel [369]

Answer:

We know that In 1990, the mean duration of long-distance telephone calls originating in one town was 7.2 minutes. And we want to test if the mean duration of long-distance phone calls has changed from the 1990 mean of 7.2 minutes (alternative hypothesis) and the complement rule would represent the null hypothesis.

The correct system of hypothesis are:

Null hypothesis: \mu =7.2

Alternative hypothesis: \mu \neq 7.2

So then the best option for this case would be:

H0: μ = 7.2 minutes Ha: μ ≠ 7.2 minutes

Step-by-step explanation:

We know that In 1990, the mean duration of long-distance telephone calls originating in one town was 7.2 minutes. And we want to test if the mean duration of long-distance phone calls has changed from the 1990 mean of 7.2 minutes (alternative hypothesis) and the complement rule would represent the null hypothesis.

The correct system of hypothesis are:

Null hypothesis: \mu =7.2

Alternative hypothesis: \mu \neq 7.2

So then the best option for this case would be:

H0: μ = 7.2 minutes Ha: μ ≠ 7.2 minutes

And in order to test the hypothesis we can use a one sample t test or z test depending if we know the population deviation or not

4 0
2 years ago
Which statements are true? Check all that apply. The equation |–x – 4| = 8 will have two solutions. The equation 3.4|0.5x – 42.1
NeX [460]

Answer:

1. The equation |-x -4| = 8 will have two solutions. (True)

5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)

Step-by-step explanation:

1. The equation |-x -4| = 8 will have two solutions. (True)

|-x - 4| = 8

-x -4 = ±8

-x -4 = 8 and -x -4 = -8

-x = 8 + 4 and -x = -8 + 4

-x = 12 and -x = -4

x = -12 and x = 4

Therefore, it has two solutions x ∈ {-12, 4}

2. The equation 3.4|0.5x - 42.1| = -20.6 will have one solution. (False)

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

3. The equation |1/2x - 3/4| = 0 will have no solutions. (False)

|(1/2)x - 3/4| = 0

(1/2)x - 3/4 = ±0

Since ±0 is the same

(1/2)x = 3/4

x = 2*3/4

x = 3/2

Therefore, it has one solution x = 3/2

4. The equation |2x – 10| = –20 will have two solutions. (False)

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)

|0.5x – 0.75| + 4.6 = 0.25

|0.5x – 0.75| = 0.25 - 4.6

|0.5x – 0.75| = -4.35

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

6. The equation |(1/8)x - 1| = 5 will have infinitely many solutions. (False)

|(1/8)x - 1| = 5

(1/8)x - 1 = ±5

(1/8)x - 1 = 5 and (1/8)x - 1 = -5

(1/8)x = 5 + 1 and (1/8)x = -5 + 1

(1/8)x = 6 and (1/8)x = -4

x = 6*8 and x = -4*8

x = 48 and x = -32

Therefore, it has two solutions x ∈ {48, -32}

4 0
2 years ago
Read 2 more answers
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