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natka813 [3]
2 years ago
11

.

Mathematics
1 answer:
saveliy_v [14]2 years ago
7 0
When you translate, you Add or Subtract a number to x and y
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Suppose that Upper X has a discrete uniform distribution f left-parenthesis x right-parenthesis equals StartLayout left-brace1st
emmasim [6.3K]

Answer:

the probability that the sample mean is greater than 2.1 but less than 2.4 is 0.2444

Step-by-step explanation:

Given the data in the question;

x        f(x)         xp(x)               x²p(x)

1         1/3        0.33333        0.33333

2        1/3        0.66667        1.33333

3        1/3        1.00000        3.0000

∑                    2.0000          4.6667

∑(xp(x)) = 2

∑(x²p(x)) = 4.6667

Variance σ² = ∑(x²) - ∑(x)² = 4.6667 - (2)² = 4.6667 - 4 = 0.6667

standard deviation σ = √variance = √0.6667 = 0.8165

Now since, n = 33 which is greater than 30, we can use normal approximation

for normal distribution z score ( x-μ)/σ

mean μ = 2

standard deviation = 0.817

sample size n = 33

standard of error σₓ = σ/√n = 0.817/√33 = 0.1422

so probability will be;

p( 2.1  < X < 2.4 ) = p(( 2.1-2)/0.1422) <  x"-μ/σₓ  <  p(( 2.4-2)/0.1422)

= 0.70 < Z < 2.81    

=  1 - ( 0.703 < Z < 2.812 )

FROM Z-SC0RE TABLE

=  1 - ( 0.25804 + 0.49752 )

= 1 - 0.75556

p( 2.1  < X < 2.4 ) = 0.2444

Therefore,  the probability that the sample mean is greater than 2.1 but less than 2.4 is 0.2444

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BTW k = -1

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