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A birth is selected at random. Define events B = {the baby is a boy} and F = {the mother had the flu during her pregnancy}. The events B and F are Disjoint but not independent.
A card is drawn at random from a standard 52-card deck. The conditional probability that the card is a 2 given that a 2 or a 3 was drawn is
Suppose two different states each pick a two-digit lottery number between 00 and 99 (for a 100 possible numbers). What is the probability that both states pick the number 13?
A standard 52-card deck is shuffled and 5 cards are picked, without replacement, from the top of the deck. The probability that the first four cards are a red suit (Heart or Diamond) and the last ca
A medical treatment has a success rate of 0.8. Two patients will be treated with this treatment. Assuming the results are independent for the two patients, what is the probability that neither one o
Elizabeth has just put 4 new spark plugs in her car. For each spark plug, the probability that it will fail in the next 50,000 miles is 1/100 (which is 0.01), and is independent from one spark plug
A survey was given to sophomores at a university and one of the questions asked was "What is the probability that you will leave school before you graduate?" The answer to this question for an indiv
A bus passes by a certain street corner every morning around 9:00 a.m. Let X be the difference (in minutes) between the time instant at which the bus passes and 9:00 a.m. We suppose that X has appro
In the formula for sample variance based on a sample of size n, why is the sum of squares divided by n-1?
A sample of size 30 from a normal population with known variance is taken. Which one of the following is most correct regarding the distribution of the standardised sample mean?
A simple random sample of size 100 is taken from a population. The population variance in unknown. The distribution of the standardised sample mean is a t-distribution. What are the degrees of freed
A population has mean 20. A simple random sample of size 100 is selected from this population. What is the mean of the sample mean?
A, B, C, and D are taking goal shots in soccer. They take shots in the order A, B, C, D, then repeat. By going in this order they have an equal chance of making a goal first.
What number of customers waiting in line does Shylock most often see the moment he enters? What is the average number of customers who are waiting in line the moment Shylock enters?
A batch contains 34 bacteria cells. Assume that 12 of the cells are not capable of cellular replication. Six cells are selected at random, without replacement, to be checked for replication. Round
A locomotive's adhesion is the locomotive's pulling force as a multiple of its weight. This is an important performance measure of a locomotive. A diesel locomotive model has adhesion that varies i
The prices of all college textbooks follow a bell-shaped distribution with a mean of $111 and a standard deviation of $19. Using the empirical rule, find the interval that contains the prices of 99.
Consider a population that consists of 600 lives aged 50 and 520 lives aged 60. Probability: one aged 50 lives to 80 p=0.43732 probability: one aged 60 lives to 80 p=0.47806 and all lives have inde
Suppose 3% of cotton fabric rolls and 3% of nylon rolls contain flaws. Of the rolls used by a manufacturer, 70% are cotton and 30% are nylon. What is the probability that a randomly selected roll us
Heart failures are due to either natural occurrences (82%) or outside factors (18%). Outside factors are related to induced substances (73%) or foreign objects (27%). Natural occurrences are caused
A player of a video game is confronted with a series of 3 opponents and a(n) 77% probability of defeating each opponent. Assume that the results from opponents are independent (and that when the pla
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:
Birthweights at a local hospital have a normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. What percentage of infants have birthweights between 125 oz and 140 oz?
Determine the selling price PV, per $1,000 maturity value, of the bond. HINT (Assume twice-yearly interest payments. Round your answer to the nearest cent.)