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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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We know that when two rational numbers is added then the sum is also a rational number. And when two rational numbers are subtracted then the difference is also a rational number.

So in the given question, lets study the term differently that is,

i) 7 - 1 is a rational number because their difference is equal to 6 and it can be written in p/q form which is 6/1.

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