A lot containing 7 components is sampled by a quality inspector; the lot contains
4 good components and 3 defective components. A sample of 3 is taken by the inspector. Find the expected value of the number of good components in this sample.
Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pens, and 3 green pens. If X is the number of blue pens selected and Y is the number of red pens selected.
If X is a continuous random variable having cumulative distribution F, then its median is defined as that value of m for which
F(m) = 1/2.
Consider the random variable with density function
f(x) = 3x2, 0≤x≤1.
An electrical firm manufactures 100-watt light bulbs. These bulbs, according to specifications written on the package, have a mean life of 900 hours with a standard deviation of 50 hours. Assume that the distribution is symmetric about the mean.
The probability that a patient recovers from a rare blood disease is 0.4. If 15 people are known to have contracted this disease, what is the probability that (a) at least 10 survive, (b) from 3 to 8 survive, and (c) exactly 5 survive? (Use a Cumulative binomial probabilities table.)
During a laboratory experiment, the average number of radioactive particles passing through a counter in 1 millisecond is 4. What is the probability that 6 particles enter the counter in a given millisecond? (Use a Cumulative binomial probabilities table.)
The average grade for an exam is 74, and the standard deviation is 7. If 12% of the class is given As, and the grades are curved to follow a normal distribution, what is the lowest possible A and the highest possible B? (Use a Cumulative binomial probabilities table.)
The length of time for one individual to be served at a cafeteria is a random variable having an exponential distribution with a mean of 4 minutes. What is the probability that a person is served in less than 3 minutes on at least 4 of the next 6 days?
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