Answer:
a)
Group 18-34 years old
Group 35-44 years old
Group 45 and older
b)
According to the sample there is 9.04% probability that a person between 18 and 34 consume less than the average, 47.74% probability that a person between 35 and 44 consume more than the average and 50% probability that a person older than 45 consume more than the average.
Step-by-step explanation:
a)
The <em>mean</em> for each sample is
where the are the data corresponding to each group
The <em>variance</em> is
and the <em>standard deviation </em>is s, the square root of the variance.
<u>Group 18-34 years old </u>
<u>Group 35-44 years old </u>
<u>Group 45 and older </u>
b)
Let's compare these averages against the general media established of $1,092 by using the corresponding z-scores
where
<em> = mean of the sample
</em>
<em> = established average
</em>
<em>s = standard deviation of the sample </em>
<em>n = size of the sample </em>
<u>z-score of Group 18-34 years old </u>
The area under the normal curve N(0;1) between -0.2286 and 0 is 0.0904. So according to the sample there is 9.04% probability that a person between 18 and 34 consume less than the average.
<u>z-score of Group 35-44 years old </u>
The area under the normal curve N(0;1) between 0 and 2.0019 is 0.4774. So according to the sample there is 47.74% probability that a person between 35 and 44 consume more than the average.
<u>z-score of Group 45 and older </u>
The area under the normal curve N(0;1) between 0 and 7.5375 is 0.5. So according to the sample there is 50% probability that a person older than 45 consume more than the average.