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1 answer:
Answer:
Point on Midline (0,3)
Maximum (9π/2,3)
Minimum (-9π/2,-3)
Step-by-step explanation:
in the given sine function which is in the form of f(x) = a sin(bx+c) +d
a = amplitude
period = frequency = 18π
Therefore b = 2π/18π = 1/9
Y intercept = vertical shift = 3
Horizontal shift = d = 0
Therefore the sine function will be
f(x) = 6 sin(x/9) + 3
Now first point on the midline is (0,3)
Second point is maximum (9π/2,9)
Third point be a minimum value ( -9π/2,-3)
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Answer:
a) The mean is 900 and the standard deviation is 15.
b) 100% probability that at least 800 students accept.
c) 0.05% probability that more than 950 will accept.
d) 94.84% probability that more than 950 will accept
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
(a) What are the mean and the standard deviation of the number X of students who accept?
. So
The mean is 900 and the standard deviation is 15.
(b) Use the Normal approximation to find the probability that at least 800 students accept.
Using continuity corrections, this is , which is 1 subtracted by the pvalue of Z when X = 799.5. So
has a pvalue of 0.
1 - 0 = 1
100% probability that at least 800 students accept.
(c) The college does not want more than 950 students. What is the probability that more than 950 will accept?
Using continuity corrections, this is , which is 1 subtracted by the pvalue of Z when X = 949.5. So
has a pvalue of 0.9995
1 - 0.9995 = 0.0005
0.05% probability that more than 950 will accept.
(d) If the college decides to increase the number of admission offers to 1300, what is the probability that more than 950 will accept?
Now n = 1300. So
Same logic as c.
has a pvalue of 0.0516
1 - 0.0516 = 0.9484
94.84% probability that more than 950 will accept
Answer:
She work <u>23 hours</u>.
Step-by-step explanation:
Given:
Tracy works at the Pizza Place. She earns $4.50 an hour plus tips.
Last week, she earned a total of $156.00, of which $52.50 was tips.
Now, to find the number of hours she work.
Total salary = $156.00
Amount of tips = $52.50.
So, first we deduct the amount of tips from the total salary:
<em>Thus, the remaining salary = $103.50.</em>
As, given salary she earns an hour = $4.50.
And then, to get the number of hours she work last week by dividing $103.50 the remaining salary by $4.50:
Therefore, she work 23 hours.