ASU Continuous Probability Density Functions Exam Practice 5 Q in Continuous Probability Density Functions HW and you could just hand write the answer in a
ASU Continuous Probability Density Functions Exam Practice 5 Q in Continuous Probability Density Functions HW and you could just hand write the answer in a pice of paper Instructions:
For full credit, you must clearly illustrate each problem on the graph provided, with labels and using terminology similar to that
used in class: F(T), F(Z), a, P(X>value), P(X=value), etc. Clearly show and label the mean, std dev, and the significant values and
areas needed to support your answer. Show any computations necessary to support your answer in the space provided. Print clearly.
Provide answers to 3-decimal place accuracy (1-decimal for percentages).
Note: you must show interpolation for problem 4; on other problems, round to nearest value on distribution table.
Hint: answers to 1 & 2 and 3 & 4 should be similar but not exactly equal.
The lifespan of a new LED bulb is being studied. Testing has determined the lifespan is approximately normally
distributed with an average of 4000 hours and a standard deviation of 75 hours.
1. Compute the 80% lifespan [that is, the 80″ percentile or P(x < X80%) = 0.80] using the normal distribution and the
provided parameters. Label the provided distribution with relevant information.
Ans:
(4 pts)
"normal"
2. Compute the 80% lifespan using the "t" distribution for a sample size of 6 along with the provided parameters. Label
the provided distribution with relevant information.
Ans:
(4 pts)
"L"
3. Using the normal distribution, what percentage of bulbs are expected to have a lifespan above 3900 hours?
normal
Ans:
(4 pts)
4. Using the "t" distribution, what percentage of bulbs (again, with a sample size of 6) are expected to have a lifespan
above 3900 hours? You will need to interpolate between relevant values on the "t" chart for probability based upon your
"t" statistic and the sample size. Show your interpolation.
Ans:
(4 pts)
5. If 91% of bulbs are expected to have a lifespan above 3750 hours, what is the probability that a sample of 28 bulbs
will have more than 21 but less than 25 bulbs having a lifespan greater than 3750 hours? For any credit, you must
use the normal approximation to the binomial distribution to solve this problem.
Ans:
(4 pts)
normal
Extra Credit: Use the Binomial to compute the exact answer to problem #5 (results should be relatively close).
Ans:
(2 pts)
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