Final answer:
To find the proportion of full-time employees earning more than $837, calculate the ratio of the number of employees with earnings > $837 to the total number of employees. For various probability calculations based on a sample of 150 employees, you can utilize the binomial distribution and compare cumulative probabilities. The unusualness of a percentage below 42% can be determined by comparing the cumulative probability to a cutoff of 0.05.
Step-by-step explanation:
A) To find the proportion of full-time employees with weekly earnings of more than $837, we need to know the total number of full-time employees. Assuming the total number is 100, the proportion can be calculated as follows:
Proportion = (Number of employees with earnings > $837) / (Total number of employees)
Assuming 70 employees earn more than $837, the proportion would be:
Proportion = 70 / 100 = 0.7
B) To find the probability that more than 55% of a sample of 150 employees earn more than $837 per week, we can use the binomial distribution. The probability can be calculated as:
Probability = 1 - cumulative probability of 55% or less
C) To find the probability that less than 59% of the sample of 150 employees earn more than $837 per week, we can again use the binomial distribution. The probability can be calculated as:
Probability = cumulative probability of 59% or less
D) To find the probability that between 44% and 59% of the sample of 150 employees earn more than $837 per week, we can subtract the cumulative probability of 44% or less from the cumulative probability of 59% or less.
E) To determine if it would be unusual for less than 42% of the sample of 150 employees to earn more than $837 per week, we can calculate the cumulative probability of 42% or less and compare it to the cutoff of 0.05. If the cumulative probability is less than 0.05, it would be considered unusual.