In: Statistics and Probability
It is known that 80% of all college professors have doctoral degrees. If 10 professors are randomly selected, find the probability that
a. fewer than 4 have doctoral degrees.
b. At least 6 have doctoral degrees.
c. Between 5 and 7 (inclusive) have doctoral degrees.
d. Calculate the mean or expected number. e. Calculate the variance and standard deviation.
In: Statistics and Probability
A lottery game is played in many places and requires $1 per ticket to play. To win the jackpot, a person must correctly pick five unique numbers from balls numbered 1 through 36 (order does not matter) and correctly pick a final number, which is chosen from balls numbered 1 through 26. What is the probability of winning the jackpot?
In: Statistics and Probability
Let X be the number of spades that show up when randomly choosing three cards from a standard 52 card deck. (without replacement). Construct a probability distribution for X on the table to the left.
Use fractions for probabilities. The find the mean and standard deviation.
| x | P(X=x) | |||
Mean: 2 Decimal Places
Standard Deviation: 2 Decimal Places
In: Statistics and Probability
In: Statistics and Probability
The photo booth at the Apple County fair takes snapshots in exactly 90 seconds. Customers arrive at the machine according to a Poisson distribution at the mean rate of 25 per hour. Using this information, determine the following:
| a. | the average number of customers waiting to use the photo machine |
| b. | the average time a customer spends in the system |
| c. | the probability an arriving customer must wait for service. |
In: Statistics and Probability
Suppose we have a biased coin that comes up heads 55% of the time. We perform an experiment where we toss the coin until the first tails appears. Let T be the number of tosses until the first tails. What is the expected value and standard deviation for T? What is the probability that it takes 5 or more tosses before the first tails appears?
In: Statistics and Probability
1. Consider the following function
F(x) = {2x / 25 0<x<5
{0 otherwise
a) Prove that f(x) is a valid probability function.
b) Develop an inverse-transformation for this function.
c) Assume a multiplicative congruential random number generator with parameters:
a: 23, m: 100, and xo: 17. Generate two random variates from the function for (x).
In: Statistics and Probability
You roll a die, winning nothing if the number of spots is even, $3 for a 1 or a 3, and $18 for a 5.
a) Find the expected value and standard deviation of your prospective winnings.
b) You play three times. Find the mean and standard deviation of your total winnings.
c) You play 30 times. What is the probability that you win at least $160?
In: Statistics and Probability
Assume that 35% of all patients in ER have COVID. Consider a random sample of 90 patients and let X denote the number among these that have COVID.
What is the probability that X is between 15 and 25 (inclusive)? What is the exact answer (use the pmf table)? What would the normal approximation predict? (You Should do this calculation by hand)? How close are these?
In: Statistics and Probability