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Basile [38]
2 years ago
11

Suppose the lifetime of a cell phone battery is normally distributed with a mean of 36 months and a standard deviation of 2 mont

hs. If the company wants to replace no more than 2% of all batteries, for how many months should they guarantee the lifetime of their batteries
Mathematics
1 answer:
solong [7]2 years ago
3 0

Answer:

They should guarantee the lifetime of their batteries for 32 months.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 36 months and a standard deviation of 2 months.

This means that \mu = 36, \sigma = 2

If the company wants to replace no more than 2% of all batteries, for how many months should they guarantee the lifetime of their batteries?

The guarantee should be the 2th percentile of lengths, which is X when Z has a pvalue of 0.02. So X when Z = -2.054.

Z = \frac{X - \mu}{\sigma}

-2.054 = \frac{X - 36}{2}

X - 36 = -2.054*2

X = 31.89

Rounding to the closest month, 32.

They should guarantee the lifetime of their batteries for 32 months.

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Fill in the missing work and justification for step 3 when solving 2(x + 1) = 10.
kirill115 [55]

Answer:

2(x + 1) = 10

x = 4

Step-by-step explanation:

Given:

2(x + 1) = 10

Solution:

Apply Distributive property

A*(B+C) = (A*B) + (A*C)

This means multiply 2 with x and 1

2*(x+1) = (2*x) + (2*1)

2x + 2 = 10      

Use Subtraction property of equality

A = B, then A - C = B - C

Subtracting 2 from both sides:

2x + 2 - 2 = 10 - 2

2x = 8                  Step 3

Use Division property of equality

It state that if you divide both sides of an equation by same nonzero number then the sides remain equal

Dividing both sides by 2

2x/2 = 8/2

x = 4

This means value of x is 4

Another method to solve this equation is:

2(x+1)=10  

Use Distributive property

A*(B+C) = (A*B) + (A*C)

2*(x+1) = (2*x) + (2*1)  

2*(x+1) = 2x + 2  

Use commutative property

A + (-B) = (-B) + A

2x + 2 + (-2) = 2x + (-2) + 2

2x + 2 + (-2) = 10 + (-2)

2x + 2 - 2 = 10-2  

2x = 8  

Using division property

AX = B  

AX / A = B / A

So

X = B/A

This becomes:

2x = 8

2x = 8.

Divide both sides by 2  

2x / 2 = 8 / 2  

x = 4

3 0
3 years ago
Suppose both the mean and median of a distribution are 24. Which of these
kow [346]

Answer:

D is the correct answer.

3 0
2 years ago
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A school wants to attract more students to its media center. The media specialist has been asked to conduct a survey to determin
aliina [53]
I would say C or B but I may be wrong
6 0
3 years ago
There are 278 houses in Hannah's neighborhood. She collected a total of $780 from her neighbors to donate for a local charity. H
ser-zykov [4K]
First, we need to find out how many houses that Hannah received money from. We can do this by dividing the total amount of money she received by the amount she received per house.

780 / 5 = 156

Hannah received money from 156 houses.
To find the amount of houses she did NOT collect money from, we just need to subtract the amount of houses that she DID receive money from away from the total amount of houses in her neighborhood.

278 - 156 = 122

Hannah did not collect money from 122 houses.
Hope this helped! =)
6 0
3 years ago
Read 2 more answers
Which equation shows the value of -2/5 - -9/15
Alika [10]

Answer:

D) 3/15

Step-by-step explanation:

(-2/5) - (-9/15) = (-6/15) - (-9/15) = (-6/15) + (9/15) = 3/15

6 0
2 years ago
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