[Q71 Suppose that the height, in inches, of a 25-year-old man is a normal random variable with parameters g = 71 inch and 02 = 6
1 answer:
Answer: (a) Percentage of 25 year old men that are above 6 feet 2 inches is 11.5%.
(b) Percentage of 25 year old men in the 6 footer club that are above 6 feet 5 inches are 2.4%.
Step-by-step explanation:
Given that,
Height (in inches) of a 25 year old man is a normal random variable with mean and variance
.
To find: (a) What percentage of 25 year old men are 6 feet, 2 inches tall
(b) What percentage of 25 year old men in the 6 footer club are over 6 feet. 5 inches.
Now,
(a) To calculate the percentage of men, we have to calculate the probability
P[Height of a 25 year old man is over 6 feet 2 inches]= P[X>]
P[X>74] = P[ >
]
= P[Z > 1.2]
= 1 - P[Z ≤ 1.2]
= 1 - Ф (1.2)
= 1 - 0.8849
= 0.1151
Thus, percentage of 25 year old men that are above 6 feet 2 inches is 11.5%.
(b) P[Height of 25 year old man is above 6 feet 5 inches gives that he is above 6 feet] = P[X,
- X,
]
P[X >
I X >
] = P[X > 77 I X > 72]
=
=
=
=
=
=
= 0.024
Thus, Percentage of 25 year old men in the 6 footer club that are above 6 feet 5 inches are 2.4%.
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where:
is the population after 
years
is the initial population
is the time in years
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is the Euler's constant
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We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.
B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
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Population in 2010: 713,777
We know from our investigation that
, 
, and . Just like before, lets replace those values into our equation to find :
= -2.9%.
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C. Final equation from point A:
.
Final equation from point B:
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D. To find the year in which the population of Orlando will exceed the population of Detroit, we are going equate both equations and and solve for t:
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where:
We now for our investigation that
Now lets multiply
We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.
B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
Population in 2000: 951,307
Population in 2010: 713,777
We know from our investigation that
We just show that Detroit's population has been declining at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.
C. Final equation from point A:
Final equation from point B:
Similarities: Both have an initial population and use the same Euler's constant.
Differences: In the equation from point A the exponent is positive, which means that the function is growing; whereas, in equation from point B the exponent is negative, which means that the functions is decaying.
D. To find the year in which the population of Orlando will exceed the population of Detroit, we are going equate both equations
We can conclude that if Orlando's population keeps growing at the same rate and Detroit's keeps declining at the same rate, after 31.36 years in May of 2031 Orlando's population will surpass Detroit's population.
E. Since we know that the population of Detroit as 2000 is 951307, twice that population will be
We can conclude that after 45 years in 2045 the population of Orlando will exceed twice the population of Detroit.