Question

The number of hours that employees work per week in Anteater company is known to follow a normal distribution with a mean of 40 hours and a standard deviation of 5 hours. 1) What is the probability that an employee selected at random from this company works overtime, defined as working more than 45 hours per week?

Answer 1

Using the Z-score for a normal distribution, the probability that an employee at Anteater company works more than 45 hours per week is approximately 15.87%.

Step-by-step explanation:

To calculate the probability that a randomly selected employee from Anteater company works more than 45 hours per week, we apply the properties of normal distribution. Given that the mean is 40 hours and the standard deviation is 5 hours, we first compute the Z-score for 45 hours using the formula:

Z = (X - μ) / σ

Where X is the value of interest (45 hours), μ is the mean (40 hours), and σ is the standard deviation (5 hours). Plugging the values in, we get:

Z = (45 - 40) / 5 = 1

Now, we look up the Z-score of 1 in the standard normal distribution table or use a normal distribution calculator to find the probability to the left of this Z-score. To find the probability of an employee working more than 45 hours, we subtract this value from 1 because we want the area to the right of the Z-score. If the standard normal table gives us a value of P(Z < 1), then:

Probability (Employee works > 45 hours) = 1 - P(Z < 1)

Assuming P(Z < 1) is approximately 0.8413, we get:

Probability (Employee works > 45 hours) = 1 - 0.8413 = 0.1587

The probability that an employee at Anteater company works overtime is approximately 15.87%.