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marissa [1.9K]
3 years ago
15

The volume of a shampoo filled into a container is uniformly distributed between 370 and 385 milliliters. (a) What are the mean

and standard deviation of the volume of shampoo? (b) What is the probability that the container is filled with less than the advertised target of 375 milliliters? (c) What is the volume of shampoo that is exceeded by 95% of the containers?
Mathematics
1 answer:
Olenka [21]3 years ago
7 0

Answer:

(a) mean = 377.5ml. standard deviation = 4.33

(b) 0.333

(c) 384.25 ml

Step-by-step explanation:

(a)The mean:

\mu = \frac{385 + 370}{2} = 377.5 ml

The standard deviation:

\sigma = \frac{385 - 370}{\sqrt{12}} = 4.33

(b)

P(x < 375) = \frac{375 - 370}{385 - 370} = \frac{1}{3} \approx 0.333

(c)P(x > m) = 0.95

\frac{m - 370}{385 - 370} = 0.95

m - 370 = 14.25

m = 384.25ml

So the volumn of shampoo should be 384.25ml to exceed 95% of containers.

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Dennis went cross country skiing for 6 hours on Saturday. He skied 20 miles uphill and then 20 miles downhill, returning to his
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Answer: Downhill:10mph   Uphill:5mph

Step-by-step explanation:  

We are looking for Dennis’s downhill speed.

Let  

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Let  

r−5=

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Since  

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t=

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We divide the distance by the rate in each row and place the expression in the time column.

Rate

×

Time

=

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Downhill

r

20

r

20

Uphill

r−5

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r−5

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Write a word sentence about the time.

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6

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Translate the sentence to get the equation.

20

r

+

20

r−5

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Solve.

20(r−5)+20(r)

40r−100

0

0

0

=

=

=

=

=

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6

r

2

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6

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r=

5

3

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5

3

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Check. Is  

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mph a reasonable speed for biking downhill? Yes.

Downhill:

10 mph

5 mph⋅

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The total time traveled was  

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Dennis’ downhill speed was  

10

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