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LenKa [72]
3 years ago
14

1. A manufacturer of a printer determines that the mean number of days before a cartridge runs out of ink is 75 days, with a sta

ndard deviation of 6 days. Assuming a normal distribution, what is the probability that the number of days will be less than 67.5 days?
Mathematics
1 answer:
satela [25.4K]3 years ago
8 0

Answer:

P(X

And we can find this probability using the normal standard table or excel:

P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the number of days before cartridge runs out of a population, and for this case we know the distribution for X is given by:

X \sim N(75,6)  

Where \mu=75 and \sigma=6

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

P(X

And we can find this probability using the normal standard table or excel:

P(z

You might be interested in
Here's the result of this question
Dafna11 [192]

We have been given that Anil borrows $80 000 to buy a business.  The bank gives him a loan, with an interest rate of 2% each year. We are asked to find the total amount paid back by Anil to bank after 10 years.

We will use simple interest formula to solve our given problem.

A=P(1+rt), where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

Let us convert 2% into decimal.

2\%=\frac{2}{100}=0.02

We have P=\$80,000 and t=10, so we will get:

A=\$80000\left(1+0.02\cdot 10\right)

A=\$80000(1+0.2)

A=\$80000(1.2)

A=\$96,000

Therefore, Anil will pay \$96,000 to the bank after 10 years.

8 0
3 years ago
A bag contains 30 red and blue marbles. If 19 are blue, what fraction of the marbles are blue?
Musya8 [376]

Answer:

19%

Step-by-step explanation:

19/100. i don't think it is that simple, but i did the best i could

5 0
2 years ago
Mr. Kennedy raise beef cattle the stock tank near the windmill has a diameter of 3 m what it is for the water is 1.5 m deep how
sergeinik [125]

Answer:

10.6

Step-by-step explanation:

radius = 1.5 height = 1.5 so it's 10.6

7 0
3 years ago
Your round trip drive to school is 3 7/10 miles.how many miles do you drive to and from school in 5 days?
riadik2000 [5.3K]

Answer:

18 1/2 miles

Step-by-step explanation:

3 7/10 * 5

Change to an improper fraction

(10* 3 + 7)/10    * 5

37/10 *5

Rewriting

37 * 5/10

37/2

Changing back to an mixed number

2 goes into 37 18 times with 1 left over

18 1/2

5 0
3 years ago
A company uses the function C(x)=20.50+2000, where C is the cost and x is the number of units it produces, to determine its dail
Kipish [7]
You left it out, but I'm thinking that there must be an 'x' next to the '20.50' in the function.  I'm so sure of it that I'll assume it, as I proceed to answer the question:

C(x) = 20.50x + 2,000

Subtract  2,000 from each side:      C - 2,000  =  20.50 x

Divide each side by  20.50 :        x  =  (C - 2,000) / 20.50

When C = $625,000 . . .

x = (625,000 - 2,000) / 20.50  =  623,000 / 20.50  =  30,390.2439

<em>30,390 complete units</em> are produced, and there are  5  bucks left over,
to split up among all the loyal employees who worked with such diligence and dedication to make it happen.  The company's senior management will graciously add each worker's share to his gross pay before taxes for the second month following the close of the current quarter, with a photocopied note inserted in the pay envelope, expressing management's sincere thanks to everyone, an admonition not to spend it all in one place, and a reminder that no matter how many festivals to their god they need to go out to the desert to celebrate, their tally of bricks for the next quarter shall not be diminished.

6 0
3 years ago
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