Question

According to a recent poll cholesterol levels in healthy adults are right skewed with a mean of 209 mg/dL and a standard deviation of 35 mg/dL. A random sample of 42 healthy adults is selected. What is the value of the sample mean cholesterol level such that 92.5% of sample mean values are below this level?

a. 158.6

b. 216.777

c. 201.223

d. 259.4

Answer #1

Solution :

Given that ,

mean = = 209

standard deviation = = 35

n = 42

_{}
=
= 209 and

_{}
=
/
n = 35 /
42 = 5.4006

The z - distribution of the 92.5% is,

P( Z < z ) = 92.5 %

P( Z < z ) = 0.925

P( Z < 1.44 ) = 0.925

z = 1.44

Using z - score formula,

= z *
_{}
+

= 1.44 * 5.4006 + 209

= **216.777**

**Option b is correct.**

According to a recent poll cholesterol levels in healthy adults
are right skewed with a mean of 209 mg/dL and a standard deviation
of 35 mg/dL. A random sample of 42 healthy adults is selected.
Describe the sampling distribution of the sample mean cholesterol
level for the sample of 42 adults.
a. X̄ ~ AN(209, 35)
b. X̄ ~ N(209, 5.4006)
c. X̄ ~ N(209, 35)
d.
X̄ ~ AN(209, 5.4006)

According to a recent poll cholesterol levels in healthy adults
are right skewed with a mean of 209 mg/dL and a standard deviation
of 35 mg/dL. A random sample of 42 healthy adults is selected.
Describe the sampling distribution of the sample mean cholesterol
level for the sample of 42 adults.
a.
X̄ ~ N(209, 5.4006)
b.
X̄ ~ N(209, 35)
c.
X̄ ~ AN(209, 5.4006)
d.
X̄ ~ AN(209, 35)

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