Answer:
The z-score (value of z) for an income of $1,100 is 1.
Step-by-step explanation:
We are given that the mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100.
<em>Let X = group of weekly incomes of a large group of executives</em>
So, X ~ N()
The z-score probability distribution for a normal distribution is given by;
Z = ~ N(0,1)
where, = mean income = $1,000
= standard deviation = $100
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, we are given an income of $1,100 for which we have to find the z-score (value of z);
So, <em><u>z-score</u></em> is given by = =
= 1
<em>Hence, the z-score (value of z) for an income of $1,100 is 1.</em>