MAT 201

The number of vacation days taken by employees of a company is normally distributed with a mean of 14 days and a standard deviation of 3 days. For the next employee, what is the probability that the number of days of vacation taken is less than 10 days? More than 21 days?

1. 👍
2. 👎
3. 👁
1. 10 days is 1.33 std below the mean
21 days is 2.33 std above the mean

1. 👍
2. 👎
2. Standard deviation
Student’s Name:
Institutional affiliation:
Date:

For the normal distribution, Pr(X<=x) =x-µ/δ in which x is the standard data point, µ represents the mean while δ is the standard deviation of the data provided.
With n=10, mean=14 and standard deviation=3,
P (x ≤ 10), z = (10-14) /3 = -4/3,
P (z ≤ -1.3333) = 9.12%
With n=21, with mean still 14 and standard deviation as 3,
P (x ≥ 21), z = (21-14)/3 = 7/3,
P (x ≥ 21) = 1 - P (x <21) = 1 - P (z < 2.3333) = .0098 or. 98%

We compare these answers to what is obtained using the normal distribution online calculator.
When using a mean of 14 and a standard deviation of 3 days, the probabilities that the number of days employees will be on vacation for less than 10 days obtained generates almost similar responses. However, deviation from the mean is higher for the population than in the sample. I.e. 11-17 days for the sample compared to 5-23 days for the population. The normal distribution online calculator generates results while taking the data as a population. The difference in variance between the two can be attributed to the fact that population standard deviation puts into consideration every data point. This ensures that there are less errors as compared to when using the sample of the population. It is thus highly recommendable to use the entire units if in need of more correct responses.

1. 👍
2. 👎

Similar Questions

1. Math

The Department manager recorded the number of sick days taken laster year by each employee, What is the mean number of days employees were sick? Round to the nearest hundredth. 2.86 days**** 2.57 days 2.43 days 2.29 days

2. Math

Ms. Carter recorded the number of sick days taken last year by each employee, as shown in the table. What is the mean number of days employees were sick? Round to the nearest hundredth A.3.63 days B.2 days C.3.22 days D.3 days

3. maths

ABC company currently has 1/4 fewer computers than it has employees,if they currently have 80 employees and they want to hire 5% more.how many computers will they need to buy to ensure that each employees has one?

4. statistics

Data on number of days of work missed and annual salary increase for a company's employees show that in general exployees who missed more days of work during the year received smaller raises than those who missed fewer days. A

1. Gr.11 Math

A large company has a phone tree to contact its employees in case of an emergency factory shutdown. Each of the five senior managers calls three eployees, who calls three other employees and so on. If the tree consists of seven

A company decides to investigate the amount of sick leave taken by its employees. A sample of seven employees yields the following number of sick leave taken in the past year 1 1 3 0 1 7 1 a. Find and interpret the range

3. math

A company has two office buildings that hold 30,000 employees. Their headquarters contains 14 times as many employees as their overseas branch. Therefore, their headquarters contains __?__ employees.

4. Statistics

The lengths of pregnancies are normally distributed with a mean of 273 days and a standard deviation of 20 days. If 64 women are randomly selected, find the probability that they have a mean pregnancy between 273 days and 275

1. Math

The charges for hiring a car from three different companies, based on the number of days for which a car is hired and/or number of kilometres for which the car is driven are as follows: Company A charges \$660 per day Company B

2. statistics

A company has 140 employees, of which 30 are supervisors. Eighty of the employees are married, and 20% of the married employees are supervisors. If a company employee is randomly selected, what is the probability that the employee

3. Statistics

20. A study involves measuring the number of days absent from work for 216 employees of a large company during the preceding year. As part of the results, the researcher reports, “The number of days absent during the preceding

4. statistics

A company decides to investigate the amount of sick leave taken by its employees. A sample of seven employees yields the following numbers of days of sick leave taken in the past. 0, 1, 4, 1,6, 2. Find and interpret the range