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lukranit [14]
3 years ago
11

The time it takes a customer service complaint to be settled at a small department store is normally distributed with a mean of

10 minutes and a standard deviation of 3 minutes. Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.
Mathematics
1 answer:
noname [10]3 years ago
5 0

Answer:

0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 10 minutes and a standard deviation of 3 minutes

This means that \mu = 10, \sigma = 3

Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.

This is 1 subtracted by the p-value of Z when X = 15, so:

Z = \frac{X - \mu}{\sigma}

Z = \frac{15 - 10}{3}

Z = 1.67

Z = 1.67 has a p-value of 0.9525.

1 - 0.9525 = 0.0475.

0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.

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Answer:

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Step-by-step explanation:

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2 years ago
A large truck has two fuel tanks, each with a capacity of 150 gallons. Tank 1 is half full, and Tank 2 is empty.
12345 [234]

Answer:

1) G(t) = 75 + \frac{23}{4}t\\

2) After 8 minutes delivering fuel the tanks will have 121 gallons of fuel

Step-by-step explanation:

1) For generating the equation we have to take into account that in the tanks there is a initial volume of fuel that corresponds to 75 gallons, as it is stated that tank one is half full. As the capacity for tank 1 is of 150 gallons, half of the tank equals to:

\frac{150}{2} = 75 gallons

Now we have to convert the rate of delivery that is expressed as a mixed number to an improper fraction so:

5\frac{3}{4} = \frac{(5x4)+3}{4} = \frac{23}{4}

Then the pumping rate is of 23/4 gallons per minute, to get how many gallons are in the tank we just need to multiply this rate by the time in minutes, and as there is an initial volume we have to add it, so we have the following equation:

G(t) = 75 + \frac{23}{4}t\\

2) To know how much fuel is in the tank after 8 minutes we have to replace this time in the previous equation so we have

G(t) = 75 + \frac{23}{4}t\\G(8) = 75 + \frac{23}{4}(8)\\G(8) = 75 + 23(2)\\G(8) = 75 + 46\\G(8) = 121 gallons

After 8 minutes delivering fuel the tanks will have 121 gallons of fuel

8 0
3 years ago
Martin used three wooden craft sticks in a sculpture design. The first stick was 9.545 millimeters wide. The second stick was 8.
grigory [225]
9.545 + 8.23 = 17.775 mm wide
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3 years ago
Read 2 more answers
Need help trigonometry<br>​
pochemuha

Answer:

The measure of angle F is 67.6°

Step-by-step explanation:

In the right triangle DEF

∵ ∠E is the right angle

∵ Side DF is opposite to ∠E

∴ DF is the hypotenuse of the triangle DEF

∵ Side EF is the adjacent side of ∠F

∵ The cosine ratio = \frac{Adjacent}{Hypotenuse}

∴ cos∠F = \frac{EF}{DF}

∵ EF = 8 units

∵ DF = 21 units

→ Substitute them in the cosine ratio above

∴ cos∠F = \frac{8}{21}

→ Use cos^{-1} to find the measure of angle F

∵ m∠F = cos^{-1}(\frac{8}{21})

∴ m∠F = 67.60731219 degrees

→ Round it the nearest tenth of a degree

∴ m∠F = 67.6°

∴ The measure of angle F is 67.6°

3 0
2 years ago
BRAINLIST AND 30 POINTS!
marta [7]

1.b)

Fred has F cards. Bill has B cards. Tim has T cards.

B + F + T = 167

B = 5F

T = 4F - 3

5F + F + 4F - 3 = 167

10F - 3 = 167

10F = 170

F = 17

Fred has 17 cards.

B = 5F = 5(17) = 85

Bill has 85 cards.

T = 4F - 3 = 4(17) - 3 = 65

Tim has 65 cards.

2.a)

length = L

width = W

L = W + 5

perimeter = 2L + 2W = 168

2L + 2W = 168

2(W + 5) + 2W = 168

2W + 10 + 2W = 168

4W = 158

W = 39.5

L = W + 5 = 39.5 + 5 = 44.5

Length = 44.5 inches

Width = 39.5 inches

2.b)

Original rectangle:

width = W

length = 2W

New rectangle:

width = W - 1

length = 2W + 4

perimeter = 198 inches

perimeter = 2L + 2W = 198

2(2W + 4) + 2(W - 1) = 198

4W + 8 + 2W - 2 = 198

6W + 6 = 198

6W = 192

W = 32

L = 2W = 64

width = 32 inches

length = 64 inches

3.a)

Now:

Sam's age = S

John's age = 3S

In 5 years:

John's age = 3S + 5

Sam's age = S + 5

3S + 5 = 2(S + 5)

3S + 5 = 2S + 10

S = 5

Sam's age is 5.

John's age is 15.

This is all I have time for now. Post the rest of the problems in a different post, and I'll try to help later.

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