A company requires its secretarial employees to demonstrate his/her ability to type more than 45 words per minute in a typing test. The incompetent employees will be terminated. Lucy's typing rate is uniformly distributed between 30 and 50 words per minute.
1. What is the probability that she can type 45 to 50 words per minute in the test?
2. What is the probability that she will be terminated?
(Please show all the calculations, not just the answers)
The requirement is X>45
1. Lucy's distribution is U(30, 50) at a range of 50-30 = 20
The proportion of 45-50 is 50-45 = 5
Thus, the probability that she can type 45 to 50 words per minute is
P = 5/20 = 1/4 = 0.25
2. The probability that she will be terminated = 1-probability ...
This solution is provided in 237 words. It uses the uniform distribution to find proportion and probability, including the likelihood of her being terminated. A reference is also provided to enhance understanding of probability and uniform distributions.