Question

Mean: 16.07 SD: 0.89

Add graphs for all probabilities below questions. Include them in the file upload for Part 1. Include parameter labels and the shaded areas labeled.

1. Find the probability that a state's living wage is more than the minimum wage of $7.25 per hour. (round to 4 decimal places).

2. Find the probability of a state's living wage being more than the poverty level of $10.60 per hour. (round to 4 decimal places).

3. We wanted to ensure that 80% of families are earning a living wage, so we need to determine what the new minimum wage should be. The corresponding wage for 80% of families earning a living wage is: $ per hour (round to 2 decimals).

4. The z-score is: (round to 2 decimals).

Answer 1

Suppose, random variable X denotes wage per hour (in dollars).

1.

Required probability is given by

     [Using R-code '1-pnorm(-9.910112)']

Corresponding graph is as follows.

2.

Required probability is given by

      [Using R-code '1-pnorm(-6.146067)']

Corresponding graph is as follows.

3.

We know,

   [Using R-code 'qnorm(1-0.80)']

Hence, 80% of families earning a minimum living wage of $ 15.32 per hour.

Corresponding graph is as follows.

4.

Corresponding z-score is -0.84.

Corresponding graph is as follows.