Number Of Vacation Days Taken By Employees Of A Company

Question

The Number Of Vacation Days Taken By Employees Of a Company Is Normall 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? Post your solutions to the problems and respond to the solutions posted by your classmates. The access code for a car's security system consists of five digits. The first digit cannot be zero and the last digit must be odd. How many different codes are available?

Dr. Jack HW Helper · Accepted Answer

Introduction Understanding probability distributions and combinatorial calculations plays a pivotal role in various fields, including human resources and security system design. This paper explores two statistical problems: computing probabilities associated with normally distributed vacation days and determining the total number of possible security codes given specific constraints. These problems not only illustrate fundamental concepts in probability and combinatorics but also demonstrate their practical applications. Part 1: Probability of Vacation Days The first problem involves a continuous probability distribution, specifically the normal distribution. The number of vacation days taken by employees is modeled as a normal distribution with a mean (μ) of 14 days and a standard deviation (σ) of 3 days. To find the probability that a randomly selected employee takes less than 10 days, and more than 21 days, we utilize the properties of the standard normal distribution (Z-distribution). 1. Calculating the probability that vacation days are less than 10 days First, we convert the raw score (X = 10 days) to a Z-score: $$ Z = \frac{X - \mu}{\sigma} = \frac{10 - 14}{3} = -\frac{4}{3} \approx -1.33. $$ Referring to Z-tables or using statistical software, the probability that Z is less than -1.33 is approximately 0.0918. This implies that there is about a 9.18% chance that an employee takes fewer than 10 days of vacation. 2. Calculating the probability that vacation days are more than 21 days Similarly, for X = 21 days: $$ Z = \frac{21 - 14}{3} = \frac{7}{3} \approx 2.33. $$ Using Z-tables or software, the probability that Z exceeds 2.33 is: \[ P(Z > 2.33) = 1 - P(Z Thus, there is approximately a 0.99% chance that an employee takes more than 21 days of vacation. Part 2: Total Possible Security Codes The second problem involves a combinatorial approach to counting possible security codes under specific constraints. 1. Constraints - The security code has five digits. -

Number Of Vacation Days Taken By Employees Of A Company

The Number Of Vacation Days Taken By Employees Of a Company Is Normall

Paper For Above instruction

Introduction

Part 1: Probability of Vacation Days

Part 2: Total Possible Security Codes

Conclusion

References