Question

1a.

Weekly paycheck: The Bureau of Labor Statistics reported that in 2016, the median weekly earnings for people employed full time in the United States was $837.

a. What proportion of full-time employees had weekly earnings of more than $837?

1b.

Stress at work: In a poll conducted by the General Social Survey, 81% of respondents said that their jobs were sometimes or always stressful. Two hundred workers are chosen at random.

b. Approximate the probability that more than 150 find their jobs stressful.

Answer 1

1a.

Median is the value which divides the data into two equal halves.

Hence,

Proportion of full-time employees had weekly earnings of more than $837 = 0.50

1b.

Required probability = P(X>150)

Here, we use Normal approximation to Binomial distribution.

So,

X follows Normal distribution with mean and standard deviation :

Using continuity correction,

We use Excel function "NORMSDIST()" as :

Probability that more than 150 find their jobs stressful = 0.981