Question

The mean systolic blood pressure of adults is 120 millimeters of mercury (mm Hg) with a standard deviation of 5.6. Assume the variable is normally distributed.

1) If an individual is randomly selected, what is the probability that the individual's systolic pressure will be between 120 and 121.8 mm Hg.

2) If a sample of 30 adults are randomly selected, what is the
probability that the **sample mean** systolic pressure
will be between 120 and 121.8 mm Hg.

**-Central Limit Theorem -**

**please solve the following problem and explain how you
approached each step (include how you solved the problem with the
calculator):**

Answer #1

Given and .

For P(x1<X<x2), use TI-83 function **normalcdf(x1,
x2, mean, sd).**

1) For individual, use and .

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2) The Central limit theorem states that the sampling distribution of the sample mean is approximately normally distributed with mean μ and standard deviation σ/√n if either n is large or population is normal.

For sample mean, use and .

No need to solve this. In calculator, you can enter this expression directly.

Assume that the mean systolic blood pressure of normal adults is
120 millimeters of mercury (mm Hg) and the population standard
deviation is 5.6. Assume the variable is normally distributed. If a
sample of 30 adults is randomly selected, find the probability that
the sample mean will be between 120-mm and 121.8-mm Hg.

Assume that the mean systolic blood pressure of normal adults is
120 millimeters of mercury (mm Hg) and the standard deviation is
5.6. Assume that the variable is normally distributed. If an
individual is selected, find the probability that the individual’s
systolic blood pressure will be between 118.4 and 121.9 mm Hg.

Assume that the mean systolic blood pressure of normal adults
is
120millimeters
of mercury (
mmHg
) and the standard deviation is
5.6
. Assume the variable is normally distributed. Round the answers
to at least
4
decimal places and intermediate
z
-value calculations to
2
decimal places.
1.If an individual is selected, find the probability that the
individual's pressure will be between
117.2
and
120mmHg
.

The systolic blood pressure X of adults in a region is normally
distributed with mean 112 mm Hg and standard deviation 15 mm
Hg.
A person is considered “prehypertensive” if his systolic blood
pressure is between 120 and 130 mm Hg.
Find the probability that the blood pressure of a randomly
selected person is prehypertensive.

Suppose the systolic blood pressure of young adults is
normally distributed with mean 120 and standard deviation 11.
(a) Find the 77th percentile of this distribution.
(b) Find the probability that a random young adult has
systolic blood pressure above 135.
(c) Find the probability that a random young adult has
systolic blood pressure within 3.3 standard deviations of the
mean.
(d) Suppose you take a sample of 8 young adults and measure
their average systolic blood pressure. Carefully jus-...

14. For women aged 18-24, systolic blood pressure (in mm Hg) are
normally distributed with a mean of 114.8 and a standard deviation
of 13.1. If 23 women aged 18-24 are randomly selected, find the
probability that their mean systolic blood pressure is between 112
and 114.8.

For women aged 18-24, systolic blood pressures (in mm Hg) are
normally distributed with a mean of 114.8 and a standard deviation
of 13.1. Hypertension is commonly defined as a systolic blood
pressure above 140.
a. If a woman between the ages of 18 and 24 is randomly
selected, find the probability that her systolic blood pressure is
greater than 140.
b. If 4 women in that age bracket are randomly selected, find
the probability that their mean systolic blood...

For women aged 18-24, systolic blood pressures (in mm Hg) are
normally distributed with a mean of 114.8 and a standard deviation
of 13.1. Hypertension is commonly defined as a systolic blood
pressure above 140. a. If a woman between the ages of 18 and 24 is
randomly selected, find the probability that her systolic blood
pressure is greater than 140. b. If 4 women in that age bracket are
randomly selected, find the probability that their mean systolic
blood...

For women aged 18 to 24, systolic blood pressure (in mm Hg) is
normally distributed with a mean of 114.8 and a standard deviation
of 13.1 (based on data from the National Health Survey).
Hypertension is commonly defined as a systolic blood pressure above
140. Let X represent the systolic blood pressure of a randomly
selected woman between the ages of 18 and 24. a. Find the
probability the mean systolic blood pressure of four randomly
selected women would fall...

For women aged 18-24, systolic blood pressures (in mm Hg) are
normally distributed with a mean of 114.8 and a standard deviation
of 13.1. If 23 women aged 18-24 are randomly selected, find the
probability that their mean systolic blood pressure is between 119
and 122.

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