Business Assignment Writing Services | Subject Business Statistics

Topic   : Normal Distribution, Poisson Distribution and Bionomial Distributions

Customer Status: Returning

Urgency: 10 Days

Pages: 4

 Writer ID. 200143 

Instructions: 1. The total time an ambulance takes to reach its destination in emergency calls is a normal variable with mean 8.9 minutes and a standard deviation 1.8 minutes. What is the probability that for any call it will take:

  1. less than 7 minutes
  2. more than 7 minutes
  3. more than 8 minutes
  4. less than 6 minutes but more than 4 minutes to reach its destination 
  • 2. It is known that 30% of new employees in a certain company leave their new jobs after one year of employment. The company has 10 new employees. 
  1. What is the probability that after one year:
  2. two of the new employees will leave the company
  3. atleast three new employees will leave the company
  4. Non of the 10 employees will leave the company
  5. all the new employees will leave the company. 
Writers Comment:Binomial distribution is used to calculate the probability of dichotomous events such as the events of success or failure, dead or alive, pass or fail, etc. 
The density is f(x)=  \binom {n} {k} p^k (1-p)^{n-k}

for k = 0, 1, 2, ..., n, where

{n\choose k}=\frac{n!}{k!(n-k)!}
This would be applied in Question two whereby the events are dichotomous.

-          The normal distribution is a probability distribution which is used to determine probabilities of continuous variables

Examples of continuous variables are

  1. oDistances
  2. oTimes
  3. oWeights
  4. oHeights
  5. oCapacity e.t.c 
f(x) = \frac{1}{\sqrt{2\pi\sigma^2}} e^{ -\frac{(x-\mu)^2}{2\sigma^2} },

where parameter μ is the mean (location of the peak) and σ 2 is the variance (the measure of the width of the distribution). The distribution with μ = 0 and σ 2 = 1 is called the standard normal. This will be applied in question 1.