Question

Please show all work to solve the following. Thank you.

Probability Theory using the addition and multiplication rules:

a. When tossing a coin what is the probability of obtaining at least 4 heads in 6 tosses of the coin?

b. There are 5 red balls and 5 green balls in an upturned hat. If you remove the balls from the hat at random what are the chances of the following?

i. the first ball is: a) red; b) green?  

ii. if the first ball was red the second ball is: a) red; b) green?

iii. that all red balls are drawn first?

iv. that the first 5 are red and the last 5 are green?

v. that the last ball drawn is green?

The Use of the Z Score Formula and Z Score Tables.

A random sample of 80 trees are aged using a coring device. It is established that their mean age is 30 years with a standard deviation of 5 years. Assuming that their ages are distributed normally, answer the following questions using the Z score formula and the Z score tables from your textbook (make sure that you show all your work in the material that you hand in):

i. What is the age range between the second and 98th percentile?

ii. What percentage has an age range between 20 and 28 years?

Answer 1

2) Solution:-

n = 80

i) The age range between the second and 98th percentile is 19.73 and 40.27.

p-value for the top 2nd percentile = 0.02

z-score for the p-value = - 2.054

By applying normal distruibution:-

x_{2nd percentile} = 19.73

p-value for the top 98th percentile = 0.98

z-score for the p-value = 2.054

By applying normal distruibution:-

x_{98th percentile} = 40.27

ii) The percentage has an age range between 20 and 28 years is 0.322.

x₁ = 20

x₂ = 28

By applying normal distribution:-

z₁ = -2.0

z₂ = - 0.40

P( -2.0 < z < - 0.40) = P(z > - 2.0) - P(z > - 0.40)

P( -2.0 < z < - 0.40) = 0.977 - 0.655

P( -2.0 < z < - 0.40) = 0.322