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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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What’s the area and the circumference of a circle with diameter 8m?
MatroZZZ [7]

Answer:

50.24

Step-by-step explanation:

8÷2 is the radius. 3.14×4^2=50.24 m^2

^= where the exponent is supposed to go

8 0
2 years ago
Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately norm
iragen [17]

Answer:

a. 0.691

b. 0.382

c. 0.933

d. $88.490

e. $58.168

f. 5th percentile: $42.103

95th percentile: $107.897

Step-by-step explanation:

We have, for the purchase amounts by customers, a normal distribution with mean $75 and standard deviation of $20.

a. This can be calculated using the z-score:

z=\dfrac{X-\mu}{\sigma}=\dfrac{85-75}{20}=\dfrac{10}{20}=0.5\\\\\\P(X

The probability that a randomly selected customer spends less than $85 at this store is 0.691.

b. We have to calculate the z-scores for both values:

z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{65-75}{20}=\dfrac{-10}{20}=-0.5\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{85-75}{20}=\dfrac{10}{20}=0.5\\\\\\\\P(65

The probability that a randomly selected customer spends between $65 and $85 at this store is 0.382.

c. We recalculate the z-score for X=45.

z=\dfrac{X-\mu}{\sigma}=\dfrac{45-75}{20}=\dfrac{-30}{20}=-1.5\\\\\\P(X>45)=P(z>-1.5)=0.933

The probability that a randomly selected customer spends more than $45 at this store is 0.933.

d. In this case, first we have to calculate the z-score that satisfies P(z<z*)=0.75, and then calculate the X* that corresponds to that z-score z*.

Looking in a standard normal distribution table, we have that:

P(z

Then, we can calculate X as:

X^*=\mu+z^*\cdot\sigma=75+0.67449\cdot 20=75+13.4898=88.490

75% of the customers will not spend more than $88.49.

e. In this case, first we have to calculate the z-score that satisfies P(z>z*)=0.8, and then calculate the X* that corresponds to that z-score z*.

Looking in a standard normal distribution table, we have that:

P(z>-0.84162)=0.80

Then, we can calculate X as:

X^*=\mu+z^*\cdot\sigma=75+(-0.84162)\cdot 20=75-16.8324=58.168

80% of the customers will spend more than $58.17.

f. We have to calculate the two points that are equidistant from the mean such that 90% of all customer purchases are between these values.

In terms of the z-score, we can express this as:

P(|z|

The value for z* is ±1.64485.

We can now calculate the values for X as:

X_1=\mu+z_1\cdot\sigma=75+(-1.64485)\cdot 20=75-32.897=42.103\\\\\\X_2=\mu+z_2\cdot\sigma=75+1.64485\cdot 20=75+32.897=107.897

5th percentile: $42.103

95th percentile: $107.897

5 0
3 years ago
Which statement is true?
defon

Answer:

b. Multiplying decimals less than one is finding a part of a part.

Step-by-step explanation:

A part of a given number implies a selected part of a given number which can be expressed as a fraction of the number. Example, the half of any number is \frac{1}{2}.

The product of a part and another part can be expressed as;

\frac{1}{3} x \frac{2}{3} = \frac{2}{9}

or,

\frac{1}{2} x \frac{1}{2} = \frac{1}{4}

or,

\frac{1}{2} x \frac{2}{3} = \frac{2}{6} = \frac{1}{3}

The three examples shows: a part x a part.

Therefore, it would be observed that multiplying decimals less than one is the same as finding a part of a part.

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What is the rule for the following sequence of numbers: 2, 7, 17, 37, ?
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Answer:

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2 years ago
Eric and Linda are paid 52.25 for they're work. Eric worked 3.5 hours, and Linda worked 2 hours. They split the money according
Ne4ueva [31]

Answer:

<u>$33.25</u>

Step-by-step explanation:

Taking Eric's hours as a ratio to the total hours :

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Multiply the ratio into the amount paid :

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<u></u>

Eric's share of the money is <u>$33.25</u>

4 0
2 years ago
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