Question

1.The height of an adult male in the United States is approximately normally distributed with a mean of 69.3 inches and a standard deviation of 2.8 inches. Find the percentile P76 for the heights of adult males in the United States.

**Round Answer to 4 decimal places.**

2. The height of an adult male in the United States is approximately normally distributed with a mean of 69.3 inches and a standard deviation of 2.8 inches. Assume that such an individual is selected at random. What is the probability that his height will be between 65.8 inches and 71.2 inches?

**Round answer to 4 decimal places.**

3.A certain standardized test has scores which range from 0 to 500, with decimal scores possible. Scores on the exam are normally distributed with a mean of 308 and a standard deviation of 45. What proportion of students taking the exam receive a score less than 361?

**Round answer to 4 decimal places.**

Answer #1

Solution:-

Given that,

mean = = 69.3 in.

standard deviation = = 2.8 in.

1) Using standard normal table,

P(Z < z) = 76%

= P(Z < z ) = 0.76

= P(Z < 0.71 ) = 0.76

z = 0.71

Using z-score formula,

x = z * +

x = 0.71 * 2.8 + 69.3

x = 71.3 in.

P76 = 71.3 in.

2) P(65.8 < x < 71.2) = P[(65.8 - 69.3)/ 2.8) < (x - ) / < (71.2 - 69.3) / 2.8 ) ]

= P(-1.25 < z < 0.68)

= P(z < 0.68) - P(z < -1.25)

Using z table,

= 0.7517 - 0.1056

= 0.6461

3) Given that ,

mean = = 308

standard deviation = = 45

P(x < 361)

= P[(x - ) / < (361 - 308) / 45]

= P(z < 1.18)

Using z table,

= 0.8810

1)
The height of an adult male in the United States is
approximately normally distributed with a mean of 69.3 inches and a
standard deviation of 2.8 inches.
Assume that such an individual is selected at random. What is
the probability that his height will be greater than 67.8
inches?
Round your answer to 4 decimal places.

3)
The height of an adult male in the United States is
approximately normally distributed with a mean of 69.3 inches and a
standard deviation of 2.8 inches.
Find the percentile P90 for the heights of adult
males in the United States.
Provided your answer in inches, rounded to 2 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.

Suppose that the heights of adult men in the United States are
normally distributed with a mean of 69 inches and a standard
deviation of
3 inches. What proportion of the adult men in United States are
at least 6 feet tall? (Hint: 6 feet =72 inches.) Round your answer
to at least four decimal places.

In the country of United States of Heightlandia, the height
measurements of ten-year-old children are approximately normally
distributed with a mean of 53.4 inches, and standard deviation of
2.8 inches.
What is the probability that a randomly chosen child has a height
of more than 59.1 inches?
(Round your answers to 3 decimal places.)

According to the National Health Survey, the heights of adult
males in the United States are normally distributed with mean 69.0
inches and a standard deviation of 2.8 inches.
(a) What is the probability that an adult male chosen at random
is between 66 and 72 inches tall? (Round your answer to five
decimal places.)
(b) What percentage of the adult male population is more than 6
feet tall? (Round your answer to three decimal places.)

The average height of an adult male in the United States is 70
inches, with a
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Approximately what proportion of males are expected to be under
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Suppose that diastolic blood pressures of adult women in the
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Round to 4 decimal places (for example 0.0048). Do not write as a
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Round your answer to one decimal place.

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