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Darina [25.2K]
3 years ago
6

A simple random sample of 100 batteries is selected from a process that produces batteries with a mean lifetime of 32 hours and

a standard deviation of 3 hours. Thus the standard deviation of the sampling distribution is equal to 0.3.
If the sample size is changed to 400, what is the new standard deviation of the sampling distribution?a. It is one‐fourth as large as when n = 100.b. It is one‐half as large as when n = 100.c. It is twice as large as when n = 100.d. It is four times as large as when n = 100.e. The value of σ does not change.
Mathematics
1 answer:
Brrunno [24]3 years ago
7 0

Answer:

.b. It is one‐half as large as when n = 100.

Step-by-step explanation:

Given that a  simple random sample of 100 batteries is selected from a process that produces batteries with a mean lifetime of 32 hours and a standard deviation of 3 hours.

i.e. s = 0.3

we obtain se of sample by dividing std devitation by the square root of sample size

i.e. s= \frac{3}{\sqrt{n} }

when n =100 this = 0.3 and

when n =400 this equals 0.15

We find that when sample size is four times as large as original, std deviation becomes 1/2 of the original

Correction option is

.b. It is one‐half as large as when n = 100.

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Answer:

Step 4: 44 32/24 - 37 15/24= 8 17/24

<u>Here we can finally find out the mistake done by Noa. The result is 7 17/24 and not 8 17/24.</u>

Step-by-step explanation:

1. Let's review carefully all the steps taken by Noa to calculate the difference of the circumferences of the two trees.

Circumference Tree 1 = 37 5/8 inches around

Circumference Tree 2 =  45 1/3 inches around

Step 1: 45 1/3- 37 5/8

The measures are correct, no issues copying them.

Step 2: 45 8/24 - 37 15/24

Noa looked for common denominators

1/3 * 8/8 = 8 /24 is correct; 5/8 * 3/3 = 15/24 is also correct.

Step 3: 44 32/24 - 37 15/24

Noa looked for making the fraction part higher on the left side:

45 8/24 = 44 32/24 is correct because 24/24 = 1

Step 4: 44 32/24 - 37 15/24= 8 17/24

<u>Here we can finally find out the mistake done by Noa. The result is 7 17/24 and not 8 17/24.</u>

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