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Sonbull [250]
3 years ago
14

The time required for a citizen to complete the 2010 U.S. Census "long" form is normally distributed with a mean of 40 minutes a

nd a standard deviation of 10 minutes. What is the third quartile (in minutes) for the time required to complete the form? Multiple Choice
a.47.50
b.44.75
c.46.75
d.52.50
Mathematics
1 answer:
nordsb [41]3 years ago
4 0

Answer:

Third quartile (Q₃) = 46.75 minutes.

Therefore, Option (c) is the correct answer.

Step-by-step explanation:

Given: Mean  (μ) = 40 minutes and S.D (σ) = 10 minutes

To find : Third quartile (Q₃) = ?

Sol: As the third quartile of normal distribution covers the 75% of the total area of the curve and first quartile covers the 25% of the total area of the curve. Then with the help of z score table, the value represented the third quartile of the normal distribution is:

Q₃ = μ + 0.675 σ

Now by substitution the value of mean and standard deviation,

Q₃ = 40 + 0.675 × (10)

Q₃ = 40 + 6.75

Q₃ = 46.75

Therefore, the third quartile (Q₃) = 46.75. So, option (c) is the correct answer.

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2 years ago
A 25% acid solution must be added to a 40% solution to get 240 liters of 30% acid solution. How many of each should be used ?
schepotkina [342]

Answer:

The number of liters of 25% acid solution = x = 160 liters

The number of liters of 40% acid solution = y = 80 liters

Step-by-step explanation:

Let us represent:

The number of liters of 25% acid solution = x

The number of liters of 40% acid solution = y

Our system of Equations =

x + y = 240 liters....... Equation 1

x = 240 - y

A 25% acid solution must be added to a 40% solution to get 240 liters of 30% acid solution.

25% × x + 40% × y = 240 liters × 30%

0.25x+ 0.4y = 72...... Equation 2

We substitute 240 - y for x in Equation 2

0.25(240 - y)+ 0.4y = 72

60 - 0.25y + 0.4y = 72

Collect like terms

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0.15y = 12

y = 12/0.15

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x = 240 - y

x = 240 liters - 80 Liters

x = 160 liters

Therefore,

The number of liters of 25% acid solution = x = 160 liters

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