Henrietta did an experiment. She started out with 700 bacteria cells. She found that the growth rate of the bacteria cells was 5
%. Sketch the graph that represents the situation. Label the y-intercept and the point that represents the projected bacteria population 20 hours from the time Henrietta started the experiment. Label your x and y axes. Show all work.
1 answer:
Answer:
The graph in the attached figure
Step-by-step explanation:
we have a exponential function of the form
where
y ---> is the population of bacteria
x ---> the number of hours
a is the initial value or y-intercept
b is the base of the exponential function
r is the rate of change
b=(1+r)
we have
so
substitute
For x=20 hours
substitute in the equation and solve for y
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Answer:
Step-by-step explanation:
Answer:
a) 95.54% or 0.9554
b) 61.08% or 0.6108
c) 33.39%
Step-by-step explanation:
It is given that the distribution of the salaries follow a normal distribution, so we will use the concept of z-scores to answer the given questions.
Mean salary = u = $ 43,256
Standard Deviation = = $ ,3150
Part a) Probability that salary is less than $ 48,600
We have to find Probability (Salary < 48600). In symbolic form we can represent this by P(X < 48600).
We can solve this problem, by converting this value to corresponding z score, and using z table to find the said probability.
The formula of z scores is:
Using the values, we get:
So, P(X < 48600) is equivalent to P(z < 1.70). Using the z-table we can find the probability of z score being less than 1.70 i.e.
P(z < 1.70) = 0.9554
Since, P(X < 48600) = P(z < 1.70), we can write:
The probability that a randomly selected sociology major received a starting salary offer less than $48,600 is 0.9554 or 95.54%
Part b) Probability that the salary is between 42,000 and 48,600
We have to find P(42000 < X < 48600). We will use the same method as used in the previous part. First we have to convert the given values to z scores.
42000 converted to z score will be:
48600 converted to z score will be:
So,
P(42000 < X < 48600) = P(-0.40 < z < 1.70)
According to the symmetry and properties of z distribution, we can write:
P(-0.40 < z < 1.70) = P(z < 1.70) - P(z < -0.40)
= 0.9554 - 0.3446
= 0.6108
Since, P(42000 < X < 48600) = P(-0.40 < z < 1.70), we can conclude:
The probability that a randomly selected sociology major received a starting salary offer between $42,000 and $48,600 is 0.6108 or 61.08%
Part c) Percentage of salaries between 36000 and 42000
We have to find P(36000 < X < 42000). This question is exactly similar to the previous one, just with the change of values. So again, first we find the z scores.
36000 converted to z score will be:
42000 converted to z score will be:
So,
P(36000 < X < 42000) = P(-2.30 < z < -0.40)
= P(z < -0.40) - P(z < -2.30)
= 0.3446 - 0.0107
= 0.3339
Since, P(36000 < X < 42000) = P(-2.30 < z < -0.40), we can conclude:
The percentage of sociology majors received a starting offer between $36,000 and $42,000 is 0.3339 (33.39%)