Question

(3 pts) For students in a certain region, scores of students on a standardized test approximately follow a normal distribution with mean μ=543.4 and standard deviation σ=30. In completing the parts below, you should use the normal curve area table that is included in your formula packet.

(a) What is the probability that a single randomly selected
student from among all those in region who took the exam will have
a score of 548 or higher?

ANSWER:

For parts (b) through (e), consider a random sample of 30 students
who took the test.

(b) The mean of the sampling distribution of x¯ is

(c) The standard deviation of the sampling distribution of x¯ is

(d) What z-score corresponds to the mean score of x¯ =
548?

ANSWER:

(e) What is the probability that the mean score x¯ of these 30
students will be 548 or higher?

ANSWER:

Answer #1

(a). It is given that

The z-score formula is given by,

(b). The mean of the sample distribution is the same as the population mean (mu)

c). Standard deviation of sampling distribution is given by the following formula,

Where n = 30

d). The formula for z-score for sampling distribution is given by

(e). We already calculated z-score in part d. Looking up the p-value for z=0.84, we find

For students in a certain region, scores of students on a
standardized test approximately follow a normal distribution with
mean ?=531.5μ=531.5 and standard deviation ?=28.1σ=28.1. In
completing the parts below, you should use the normal curve area
table that is included in your formula packet.
(a) What is the probability that a single randomly selected
student from among all those in region who took the exam will have
a score of 536 or higher?
ANSWER:
For parts (b) through (e),...

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ANSWER:
For parts (b) through (d), consider a simple random sample (SRS)
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(b) What are the mean and standard deviation of the sample mean
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(a) What is the probability that a single student randomly
chosen from all those who took the test had a score of 555 or
higher?
ANSWER:
For parts (b) through (d), consider a simple random sample of 35
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(b) The mean of the sampling distribution of x¯x¯ is:
The standard deviation of the sampling distribution...

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consider a simple random sample (SRS) of 30 students who took
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The standard deviation of the sampling distribution for ?¯
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What is the probability that the mean score ?¯ of these students
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Find the standard deviation of the sampling distribution from
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Round your answer to 4 decimal places.

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