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Blizzard [7]
3 years ago
5

A woman has a total of

Mathematics
2 answers:
seropon [69]3 years ago
8 0

$4,000 in the 10% per year account

$11,000 in the 12% per year account

ahrayia [7]3 years ago
5 0

Answer:

4000 for 10% a year

11000 for 12% a year

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Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal prob
Novay_Z [31]

Answer:

a) By the Central Limit Theorem, it is approximately normal.

b) The standard error of the distribution of the sample mean is 1.8333.

c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours

e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 36 hours and a standard deviation of 5.5 hours.

This means that \mu = 36, \sigma = 5.5

a. What can you say about the shape of the distribution of the sample mean?

By the Central Limit Theorem, it is approximately normal.

b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

Sample of 9 means that n = 9. So

s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333

The standard error of the distribution of the sample mean is 1.8333.

c. What proportion of the samples will have a mean useful life of more than 38 hours?

This is 1 subtracted by the pvalue of Z when X = 38. So

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

By the Central Limit Theorem

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

Z = \frac{38 - 36}{1.8333}

Z = 1.09

Z = 1.09 has a pvalue of 0.8621

1 - 0.8621 = 0.1379

0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d. What proportion of the sample will have a mean useful life greater than 34.5 hours?

This is 1 subtracted by the pvalue of Z when X = 34.5. So

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

Z = \frac{34.5 - 36}{1.8333}

Z = -0.82

Z = -0.82 has a pvalue of 0.2061.

1 - 0.2061 = 0.7939

0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.

e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?

pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So

0.8621 - 0.2061 = 0.656

0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

4 0
2 years ago
Wyatt invests $1200 into an account that earns 6.2% simple interest for 4 years. He does not make any other deposits or withdraw
iVinArrow [24]

Answer:

297.60 & 1497.60

Step-by-step explanation:

I had the question before and got it right

4 0
2 years ago
Read 2 more answers
Simplify 2x + 1 - x +2.​
Pavlova-9 [17]

Answer:

the answer is x + 3

Step-by-step explanation:

7 0
3 years ago
How many solutions does the following have. Y=3x-2 and 2x+5y=7
bezimeni [28]
One, the intersection point is (1,1)
3 0
2 years ago
John and will ran for 6th grade class president.there were 36 students voting. John got two votes for every vote will got. How m
labwork [276]
Will got 12 and John got 24.

You would set the equation as:

36=n+2n

Combine like terms

36=3n

Divide 3 from both sides

12=n

If you want to check it

12+2(12)=36

12+24=36

36=36
3 0
3 years ago
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