Acme typically produces three engines per day. Some of the engines pass the quality control inspection on the first try and are ready to be shipped; others need to be retooled. The probability of an engine needing further work is 0.05. If the engine is ready to be shipped, the company makes a profit of $10,000. If it needs to be retooled, it ultimately costs the company $2000.
(a) Find the pmf of the number of engines that are ready to be shipped.
(b) Find the pmf of the company's daily profit for the plant.
(c) Find the expected profit.
In: Finance
Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 192 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.29?
Note: You should carefully round any z-values you calculate to 4
decimal places to match wamap's approach and calculations.
Answer = (Enter your answer as a number accurate to 4 decimal
places.)
In: Statistics and Probability
A fair 4-sided die is rolled, let X denote the outcome. After that, if X = x, then x fair coins are tossed, let Y denote the number of Tails observed. a) Find P( X >= 3 | Y = 0 ). b) Find E( X | Y = 2 ). “Hint”: Construct the joint probability distribution for ( X, Y ) first. Write it in the form of a rectangular array with x = 1, 2, 3, 4 and y = 0, 1, 2, 3, 4.
In: Statistics and Probability
In a group of 12 astronauts, 5 of them are experts in exobiology. Out of the 12 astronauts, 3 are randomly selected (without replacement) to be on the next mission. Let X be the number of experts selected for the mission:
a) Find the probability mass function of X (i.e. Fill out your final answers in the table):
|
x |
|
|
P (X = x) |
b) Based on your answer in a) find V ar(1.3 − 6.2X). Circle your final answer. Hint: It may be helpful to first find Var(X).
In: Statistics and Probability
A recent study has shown that 28% of 18-34 year olds check their
Facebook/Instagram feeds before getting out of bed in the
morning,
If we sampled a group of 150 18-34 year olds, what is the
probability that the number of them who checked their social media
before getting out of bed is:
a.) At least 31?
b.) No more than 52?
c.) between 36 and 44 (including 36 and 44)?
Use the Normal Approximation to the Binomial distribution to answer
this question.
In: Statistics and Probability
The huge market that exists for golf balls can be partially attributed to the fact that golfers lose them at an average rate of 3 per 18-hole round. Assume that the number of golf balls lost in an 18-hole round is distributed as a Poisson random variable. What is the probability that: No balls will be lost in an 18-hole round? 5 or fewer will be lost in an 18-hole round? 2 or fewer will be lost in a 9-hole round? 3 or fewer will be lost in a 36-hole round?
In: Statistics and Probability
1) You and a friend are talking about the probability of getting a heads on a single toss of a fair coin. Your friend insists that you are more likely to get a heads on a single toss of a fair coin than a tails. Is your friend correct, why or why not? If we were to toss the fair coin an infinite number of times, what would we expect?
2) What does it mean for two probabilities to be mutually exclusive? Provide an example of probabilities that are mutually exclusive.
In: Math
A major hurricane has wind speeds of 111 miles per hour or greater. During the 20th century, the mean number of major hurricanes to strike the U.S. mainland per year was about 0.7. Find the probability that in a given year (a) exactly one major hurricane will strike the U.S. mainland, (b) at most one major hurricane will strike the U.S. mainland and (c) more than one major hurricane will strike the U.S. mainland (Source: National Hurricane Center)
In: Economics
Customers at the local Subway store order an ice tea with their meal 75% of the time. Use the Binomial distribution to find the answer to the following. __________
Find the probability that among the next 8 customers, at least 3 will order ice tea with their meal: Of the next 8 customers, how many do you expect to order ice tea with their meal? __________
What is the standard deviation of the number of customers that order ice tea among the next 8 customers? (to two places after the decimal) _______
In: Math
Based on historical data, your manager believes that 44% of the company's orders come from first-time customers. A random sample of 141 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.26 and 0.48?
Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations. Answer = (Enter your answer as a number accurate to 4 decimal places.)
In: Math