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Answer:
(1) The probability that the time to deliver a pizza is at least 32 minutes is 0.70.
(2a) The percentage of results more than 45 is 79.67%.
(2b) The percentage of results less than 85 is 91.77%.
(2c) The percentage of results are between 75 and 90 is 15.58%.
(2d) The percentage of results outside the healthy range 20 to 100 is 2.64%.
Step-by-step explanation:
(1)
Let <em>Y</em> = the time taken to deliver a pizza.
The random variable <em>Y</em> follows a Uniform distribution, U (20, 60).
The probability distribution function of a Uniform distribution is:
Compute the probability that the time to deliver a pizza is at least 32 minutes as follows:
Thus, the probability that the time to deliver a pizza is at least 32 minutes is 0.70.
(2)
Let <em>X</em> = results of a certain blood test.
It is provided that the random variable <em>X</em> follows a Normal distribution with parameters and
.
The probabilities of a Normal distribution are computed by converting the raw scores to <em>z</em>-scores.
The <em>z</em>-scores follows a Standard normal distribution, N (0, 1).
(a)
Compute the probability that the results are more than 45 as follows:
The percentage of results more than 45 is:
Thus, the percentage of results more than 45 is 79.67%.
(b)
Compute the probability that the results are less than 85 as follows:
The percentage of results less than 85 is:
Thus, the percentage of results less than 85 is 91.77%.
(c)
Compute the probability that the results are between 75 and 90 as follows:
The percentage of results are between 75 and 90 is:
Thus, the percentage of results are between 75 and 90 is 15.58%.
(d)
Compute the probability that the results are between 20 and 100 as follows:
Then the probability that the results outside the range 20 to 100 is: .
The percentage of results outside the range 20 to 100 is:
Thus, the percentage of results outside the healthy range 20 to 100 is 2.64%.