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lorasvet [3.4K]
3 years ago
7

The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.2 grams with a standard deviat

ion of 0.18 grams. Enter your responses as a decimal with 4 decimal places. (a) What is the probability that a randomly chosen mouse has a mass of less than 19.99 grams?
Mathematics
1 answer:
Sophie [7]3 years ago
6 0

Answer:

12.1%

Step-by-step explanation:

Given that:

Mean (μ) = 20.2 grams and standard deviation (σ) = 0.18 grams.

The z score is a score used to determine the number of standard deviations by which the raw score is above or below the mean. A positive z score means  that the raw score is above the mean and a negative z score means that the raw score is below the mean. It is given by:

z=\frac{x-\mu}{\sigma}

a) For x < 19.99 g:

z=\frac{x-\mu}{\sigma}\\\\z=\frac{19.99-20.2}{0.18} \\\\z=-1.17

From the normal distribution table, P(x < 19.99) = P(z < -1.17) = 0.1210 = 12.1%

The probability that a randomly chosen mouse has a mass of less than 19.99 grams is 12.1%

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Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10
zvonat [6]

The approximate difference in the ages of the two cars, which  depreciate to 60% of their respective original values, is 1.7 years.

<h3>What is depreciation?</h3>

Depreciation is to decrease in the value of a product in a period of time. This can be given as,

FV=P\left(1-\dfrac{r}{100}\right)^n

Here, (<em>P</em>) is the price of the product, (<em>r</em>) is the rate of annual depreciation and (<em>n</em>) is the number of years.

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%.

Suppose the original price of the first car is x dollars. Thus, the depreciation price of the car is 0.6x. Let the number of year is n_1. Thus, by the above formula for the first car,

0.6x=x\left(1-\dfrac{10}{100}\right)^{n_1}\\0.6=(1-0.1)^{n_1}\\0.6=(0.9)^{n_1}

Take log both the sides as,

\log 0.6=\log (0.9)^{n_1}\\\log 0.6={n_1}\log (0.9)\\n_1=\dfrac{\log 0.6}{\log 0.9}\\n_1\approx4.85

Now, the second car depreciates at an annual rate of 15%. Suppose the original price of the second car is y dollars.

Thus, the depreciation price of the car is 0.6y. Let the number of year is n_2. Thus, by the above formula for the second car,

0.6y=y\left(1-\dfrac{15}{100}\right)^{n_2}\\0.6=(1-0.15)^{n_2}\\0.6=(0.85)^{n_2}

Take log both the sides as,

\log 0.6=\log (0.85)^{n_2}\\\log 0.6={n_2}\log (0.85)\\n_2=\dfrac{\log 0.6}{\log 0.85}\\n_2\approx3.14

The difference in the ages of the two cars is,

d=4.85-3.14\\d=1.71\rm years

Thus, the approximate difference in the ages of the two cars, which  depreciate to 60% of their respective original values, is 1.7 years.

Learn more about the depreciation here;

brainly.com/question/25297296

4 0
2 years ago
4. Identify the graph of the solution set of 9 &gt; 3 + 2x.
Ray Of Light [21]

Answer:

A

Step-by-step explanation:

9 > 3 + 2x

6 > 2x

3 > x

or

x < 3

and that means 3 is NOT included (otherwise there must be a smaller or equal sign). hence A is the right answer.

7 0
3 years ago
A 12 pack of soda is roughly $2.52. What is the cost per one can of soda?
Natalka [10]

Answer:

$2.52/12= $.21

the cost of one can of soda is $.21

Step-by-step explanation:

6 0
3 years ago
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You multiply 3.14 by the diameter or 2 times the radius 
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3 years ago
Douglas is inviting some friends to his birthday party, and
mote1985 [20]

Answer:

$91/$15=x

Step-by-step explanation:

$100-$9=$91 and 91÷15= 6. omething which means only 6 pizza can be purchased.

The answer up above just says 91 divided by 15 gives you the amount of pizzas. He can only buy 6 pizzas with a pound remainding

8 0
3 years ago
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