Recently, a random sample of 13-18 year olds was asked, "How much do you currently have in savings?" The data in the table re
present the responses to the survey. Approximate the mean and standard deviation amount of savings.
1 answer:
Answer:
μ = 235.38
σ = 234.54
Step-by-step explanation:
Assuming the table is as follows:
This is an example of grouped data, where a range of values is given rather than a single data point. First, find the total frequency.
n = 339 + 86 + 55 + 18 + 11 + 8 + 3
n = 520
The mean is the expected value using the midpoints of each range.
μ = (339×100 + 86×300 + 55×500 + 18×700 + 11×900 + 8×1100 + 3×1300) / 520
μ = 122400 / 520
μ = 235.38
The variance is:
σ² = [(339×100² + 86×300² + 55×500² + 18×700² + 11×900² + 8×1100² + 3×1300²) − (520×235.38²)] / (520 − 1)
σ² = 55009.7
The standard deviation is:
σ = 234.54
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A. The city we will use is Orlando, Florida, and we are going to examine its population growth from 2000 to 2010. According to the census the population of Orlando was 192,157 in 2000 and 238,300 in 2010. To examine this population growth period, we will use the standard population growth equation 
where:
is the population after 
years
is the initial population
is the time in years
is the growth rate in decimal form
is the Euler's constant
We now for our investigation that
, 
, and 
; lets replace those values in our equation to find :
Now lets multiply by 100% to obtain our growth rate as a percentage:
=2.2%
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
, 
, and . Just like before, lets replace those values into our equation to find :
= -2.9%.
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 and and solve for t:
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
. Now we can rewrite our equation as: 
. The last thing we need to do is equate our Orlando's population growth equation with this new one and solve for t:
We can conclude that after 45 years in 2045 the population of Orlando will exceed twice the population of Detroit.
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.
Step-by-step explanation:
here ( + ) × ( - ) = ( - )