Question

Assume that the heights of 5-year-old females is normally distributed with a population mean height of all 5-year-old females is 42.2 anda standard deviation of 3.13.

What is the mean and the standard deviation of the sample mean of 10 girls? (Round to 4 decimal places)

Find the probability that the mean height of 10 girls is greater than 45 inches. (Round to 4 decimal places) Input the StatCrunch output in SHOW YOUR WORK.

Answer #1

In a large city, the heights of 10-year-old children are
approximately normally distributed with a mean of 53.7 inches and
standard deviation of 3.7 inches.
(a) What is the probability that a randomly chosen 10-year-old
child has a height that is less than than 50.35 inches? Round your
answer to 3 decimal places.
(b) What is the probability that a randomly chosen 10-year-old
child has a height that is more than 53.2 inches? Round your answer
to 3 decimal places.

Assume that the heights of men are normally distributed with a
mean of 70.8 inches and a standard deviation of 4.5 inches. If 45
men are randomly selected, find the probability that they have a
mean height greater than 72 inches.
(Round
your answer to three decimal
places.)

Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 65 inches and standard
deviation 4 inches.
(a) What is the probability that an 18-year-old man selected at
random is between 64 and 66 inches tall? (Round your answer to four
decimal places.)
(b) If a random sample of eleven 18-year-old men is selected, what
is the probability that the mean height x is between 64
and 66 inches? (Round your answer to four decimal
places.)

15) Assume that the height of adult females in the United States
is approximately normally distributed with a mean of 64.1 inches
and a standard deviation of 2.86 inches. A sample of 8 such women
is selected at random. Find the probability that the mean height of
the sample is greater than 63.5 inches.
Round your answer to 4 decimal places.

Assume that the heights of men are normally distributed with a
mean of 68.1 inches and a standard deviation of 2.1 inches. If 36
men are randomly selected, find the probability that they have a
mean height greater than 69.1 inches. Round to four decimal
places.

Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 69 inches and standard
deviation 6 inches.
(b) If a random sample of twenty-seven 18-year-old men is selected,
what is the probability that the mean height x is between
68 and 70 inches? (Round your answer to four decimal
places.)

Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 66 inches and standard deviation 2
inches. (a) What is the probability that an 18-year-old man
selected at random is between 65 and 67 inches tall? (Round your
answer to four decimal places.) (b) If a random sample of fourteen
18-year-old men is selected, what is the probability that the mean
height x is between 65 and 67 inches? (Round your answer to four
decimal places.)

Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 71 inches and standard deviation 4
inches. If a random sample of twenty-eight 18-year-old men is
selected, what is the probability that the mean height x is between
70 and 72 inches?

The heights of 18-year-old men are normally distributed, with a
mean of 68 inches and a standard deviation
of 3 inches. If a random sample of 45 men in
this age group is selected, what is the probability that the sample
mean is between 66 and 67.6 inches?

The heights of students in a 5th grade class are
normally distributed with mean height 45 inches and standard
deviation 5 inches. The students are divided into groups of 3. What
height is such that the probability that the total height for a
given group exceeds that height is 5%?

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