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Triss [41]
1 year ago
14

A researcher collects a simple random sample of​ grade-point averages of statistics​ students, and she calculates the mean of th

is sample. Under what conditions can that sample mean be treated as a value from a population having a normal​ distribution?
a. The sample has more than 30 grade-point averages.
b. If the population of grade-point averages has a normal distribution c. The researcher collects more than 30 samples.
d. If the population of statistics students has a normal distribution.
Mathematics
1 answer:
anyanavicka [17]1 year ago
7 0

Answer:

a. The sample has more than 30 grade-point averages.

Step-by-step explanation:

Given that a researcher collects a simple random sample of​ grade-point averages of statistics​ students, and she calculates the mean of this sample

We are asked to find the conditions under which  that sample mean can be treated as a value from a population having a normal​ distribution

Recall central limit theorem here

The central limit theorem states that the mean of all sample means will follow a normal distribution irrespective of the original distribution to which the data belonged to provided that

i) the samples are drawn at random

ii) The sample size should be atleast 30

Hence here we find that the correct conditions is a.

Only option a is right

a. The sample has more than 30 grade-point averages.

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the store is 1/3 the way to her friend's house, not 1/3 mile.

this explains solution:

1/3x = 1/4

x = 1/4 * 1/3

x = 3/4

Notes:

X: is the total distance.

1/3 is the one portion of total distance.

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A park ranger spent $208 to buy 12 trees.
mixas84 [53]

Let x represent number of redwood trees and y represent number of spruce trees.

We have been given that a park ranger bought 12 trees. We can represent this information in an equation as:

x+y=12...(1)

y=12-x...(1)

We are also told that redwood trees cost $24 each, so cost of x redwood trees would be 24x.

Each spruce tree costs $16, so cost of y spruce trees would be 16y.

Since the park ranger spent $208 on trees, so we can represent this information in an equation as:

24x+16y=208...(2)

Upon substituting equation (1) in equation (2), we will get:

24x+16(12-x)=208

24x+192-16x=208

8x+192=208

8x+192-192=208-192

8x=16

\frac{8x}{8}=\frac{16}{8}

x=2

Therefore, the park ranger bought 2 redwood trees.

Upon substituting x=2 in equation (1), we will get:

y=12-x\Rightarrow 12-2=10

Therefore, the park ranger bought 10 spruce trees.

3 0
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Determine the standard form of the equation of the line that passes through (-7,8) and (0,2)
SpyIntel [72]

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6 0
1 year ago
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If f (x) = 5 x minus 25 and g (x) = one-fifth x + 5, which expression could be used to verify g(x) is the inverse of f(x)?
Vinil7 [7]

Answer:

The expression used to represent g(x) as inverse of f(x) is \frac{1}{5}(5x-25)+5

Option B is correct.

Step-by-step explanation:

We are given:

f(x)= 5x-25\\g(x)=\frac{1}{5}x+5

We need to find the expression that could be used to verify g(x) is the inverse of f(x).

We know that g(f(x))=x is inverse of function

So placing value of f(x) in g(x)

g(f(x))=\frac{1}{5}(5x-25)+5

So, the expression used to represent g(x) as inverse of f(x) is \frac{1}{5}(5x-25)+5

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We can also solve to prove that g(f(x))=x

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5 0
1 year ago
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