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Reika [66]
3 years ago
14

Suppose a random sample of 25 students is selected from a community college where the scores in the final exam (out of 125 point

s) are normally distributed, with mean equal to 112 and standard deviation equal to 12. What is the mean of the sampling distribution of the sample mean *? What is the standard deviation? Find the probability that * exceeds 116. Find the probability that the sample mean deviates from the population mean = 112 by no more than 4.
Mathematics
1 answer:
BartSMP [9]3 years ago
6 0

Answer:

he probability that the sample mean deviates from the population mean = 112 by no more than 4= 0.9050

Step-by-step explanation:

mean = 112

sd = 12/sqrt(25) = 2.4

z = (x - μ)/σ

z = (116 - 112)/2.4 = 1.67

Therefore,

P(X >= 116) = P(z <= (116 - 112)/2.4)

= P(z >= 1.67)

= 1 - 0.9525

= 0.0475

z = (x - μ)/σ

z1 = (108 - 112)/2.4 = -1.67

z2 = (116 - 112)/2.4 = 1.67

Therefore, we get

P(108 <= X <= 116) = P((116 - 112)/2.4) <= z <= (116 - 112)/2.4)

= P(-1.67 <= z <= 1.67) = P(z <= 1.67) - P(z <= -1.67)

= 0.9525 - 0.0475

= 0.9050

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Trapezoidal is involving averageing the heights
the 4 intervals are
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the area of each trapezoid is (v(t1)+v(t2))/2 times width

for the first interval
the average between 0 and 0.4 is 0.2
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4(0.2)=0.8

2nd
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3.2 times 0.7=2.24

3rd
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8 0
3 years ago
2. The table below shows that the distance d varies directly as the time t. Find the constant of variation and the equation whic
Artemon [7]
<h2><u>Problem Solving</u>:-</h2>

2. The table below shows that the distance d varies directly as the time t. Find the constant of variation and the equation which describes the relation.

<h2><u>Solution</u>:-</h2>

Since the distance d varies directly as the time t, then d = kt.

Using one of the pairs of values, (2, 20), from the table, substitute the values of d and t in d = kt and solve for k.

\sf{\rightarrow{d =  kt}}

\sf\rightarrow{20  = 2k }

\sf\rightarrow{K= \frac{20}{2} }

\sf\rightarrow{K={\color{magenta}{10}}}

<h2><u>Answer</u>:-</h2>
  • Therefore, the constant of variation is 10.
3 0
2 years ago
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