Question

In the United States, males between the ages of 40 and 49 eat on average 103.1 g of fat every day with a standard deviation of 4.32 g. The amount of fat a person eats is not normally distributed. A random sample of 33 men age 40-59 in the U.S. is taken.

It is possible with rounding for a probability to be 0.0000.

a) Identify the individual, variable, type of variable and the random variable X in the context of this problem. The individual is ________________

The variable information collected from each individual is _________________

This variable is a ___________- variable.

The random variable X is as follows: _____________________

b) List the givens with the correct symbols.

? = 103.1 g

? = 4.32 g

? = 33

c) Identify the random variable ¯¯¯ X in the context of this problem. __________________________

d) Find the mean of the sampling distribution of the sample mean. Put the numeric value in the first box and the correct units in the second box.

e) Find the standard deviation of the sampling distribution of the sample mean. Put the numeric value rounded to two decimal places in the first box and the correct units in the second box.

f) What is the shape of the sampling distribution of the sample mean? _________________

Check all that apply:

σ is unknown

σ is known

n is at least 30

population is not normal

n is less than 30

population is normal

g) Find the probability that the sample mean fat consumption of the 33 randomly selected males in the US age 40 to 49 is less than 104.1 g.

Round final answer to 4 decimal places.

DO NOT use the rounded standard deviation from part e in this computation.

Use the EXACT value of the standard deviation with the square root.

h) Find the probability that the sample mean fat consumption of the 33 randomly selected males in the US age 40 to 49 is less than 101.6 g.

Round final answer to 4 decimal places.

DO NOT use the rounded standard deviation from part e in this computation.

Use the EXACT value of the standard deviation with the square root.

i) Is a mean fat consumption of 101.6 g unusually low for 33 randomly selected males in the US age 40 to 49?___________________________

j) If you found a mean fat consumption for a sample of 33 males in the US age 40 to 49 as low as 101.6 g, what might you conclude? _____________________

Answer 1

(a)

The individual is males between the ages of 40 and 49

The variable information collected from each individual is The amount of fat a person eats

This variable is a continuous variable.

(b)

= 103.1 g

= 4.32 g

n = 33

(c)

X = The amount of fat a person eats

(d)

= the mean of the sampling distribution of the sample mean = 103.1 g

(e)

SE = the standard deviation of the sampling distribution of the sample mean = / = 4.32/ = 0.75 g²

(f)

the shape of the sampling distribution of the sample mean : Normal Distribution

σ is known

n is at least 30

(g)

= 103.1 g

= 4.32 g

n = 33

SE = 0.7520

To find P(<104.1):

Z = (104.1 - 103.1)/0.7520

= 1.3298

By Technology, Cumulative Area Under Standard Normal Curve = 0.9082

So,

P(<104.1) = 0.9082

So,

Answer is:

0.9082

(h)

(g)

= 103.1 g

= 4.32 g

n = 33

SE = 0.7520

To find P(<101.6):

Z = (101.6 - 103.1)/0.7520

= - 1.9947

By Technology, Cumulative Area Under Standard Normal Curve = 0.0230

So,

P(<101.6) = 0.0230

So,

Answer is:

0.0230

(i)

A mean fat consumption of 101.6 g is unusually low for 33 randomly selected males in the US age 40 to 49 because P(<101.6) = 0.0230 is less than 5%

(j) We conclude that a sample of 33 males in the US age 40 to 49 as low as 101.6 g, does not come from population of males between the ages of 40 and 49 eat on average 103.1 g of fat every day with a standard deviation of 4.32 g.