Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α= 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter λ = 8t.
(a) What is the probability that exactly 6 small aircraft arrive during a 1-hour period? At least 6? At least 10?
(b) What are the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period?
(c) What is the probability that at least 20 small aircraft arrive during a 2.5-hour period? That at most 10 arrive during this period?
In: Statistics and Probability
A geologist has collected 14 specimens of basaltic rock and 14 specimens of granite. The geologist instructs a laboratory assistant to randomly select 23 of the specimens for analysis.
(a)
What is the pmf of the number of granite specimens selected for analysis? (Round your probabilities to four decimal places.)
| x | ||||||
| p(x) |
(b)
What is the probability that all specimens of one of the two types of rock are selected for analysis? (Round your answer to four decimal places.)
(c)
What is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value? (Round your answer to four decimal places.)
In: Statistics and Probability
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 17 days and a standard deviation of 4 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places unless instructed otherwise.
a. What is the distribution of X? X ~ N( , )
b. If one of the trials is randomly chosen, find the probability that it lasted at least 14 days.
c. If one of the trials is randomly chosen, find the probability that it lasted between 20 and 25 days.
d. 90% of all of these types of trials are completed within how many days? (Please enter a whole number)
In: Statistics and Probability
In the NBA LeBron James had a free throw success percentage of 68.9% for the 2016-17 season. If during a game, LeBron shot 6 free throws, find the probability that he
a) Made exactly 4 free throws
b) Made at least 3 free throws
c)If over the course of a season LeBron shoots 600 free throws, find the mean and standard deviation of the probability distribution for the number of free throws he makes. Mean: Standard Deviation:
d) Use the range rule of thumb to determine what range would you expect the number of successful free throws over the season.
In: Statistics and Probability
Suppose that the duration of a particular type of criminal trial
is known to be normally distributed with a mean of 17 days and a
standard deviation of 6 days. Let X be the number of days for a
randomly selected trial. Round all answers to 4 decimal places
where possible.
a. What is the distribution of X? X ~ N(,)
b. If one of the trials is randomly chosen, find the probability
that it lasted at least 13 days.
c. If one of the trials is randomly chosen, find the probability
that it lasted between 18 and 24 days.
d. 87% of all of these types of trials are completed within how
many days? (Please enter a whole number)
In: Statistics and Probability
A recent survey in Spain revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 120 km per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on 311 where the speed limit is 120 km per hour. Let X denote the number of vehicles that were exceeding the limit. a. What is the distribution of X? b. Find P(X = 10). c. Find the probability that the number of vehicles exceeding the speed limit is between 4 and 9(exclusive) d. Find the probability that two of the recorded vehicles were exceeding the speed limit
In: Statistics and Probability
A playlist contains 15 songs, 5 songs from Artist 1, 5 songs from Artist 2, and 5 songs from Artist 3. Shuffle the playlist (randomly) and listen to the first 6 songs on the playlist. Let Y1 be the number of songs from Artist 1 in the first 6 songs played and let Y2 be the number of songs from Artist 2 in the first 6 songs played.
(a) Find the joint probability distribution function for Y1 and Y2.
(b) Find the marginal probability distribution functions for Y1 and Y2. Both distributions are the same as one we have studied in the past. What is the distribution and parameters?
In: Statistics and Probability
The probability that a person suffers from migraine has relief
with a specific drug is 0.9, three people are randomly selected
with migraine to which the drug is administered. Find the
probability that the number of people achieving relief will
be:
a) Does it meet the characteristics of a binomial variable? Yes or
no,
b) No person
c) Exactly 1
d) More than one
e) Two or less
f) Two or three
g) At least 3
h) What is the expected value of the number of people achieving
relief in the sample and what is their standard deviation?
Answers yes, 0.001, 0.027, 0.972, 0.271, 0.972 0.729, 2.7 expected
value and standard deviation is 0.5196
In: Statistics and Probability
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 17 days and a standard deviation of 6 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(___,___)
b. If one of the trials is randomly chosen, find the probability that it lasted at least 15 days.
c. If one of the trials is randomly chosen, find the probability that it lasted between 20 and 23 days.
d. 62% of all of these types of trials are completed within how many days? (Please enter a whole number)
In: Statistics and Probability
The admissions office of a small college is asked to accept deposits from a number of qualified prospective freshmen so that, with probability about 0.95, the size of the freshman class will be less than or equal to 1,100. Suppose the applicants constitute a random sample from a population of applicants, 80% of whom would actually enter the freshman class if accepted. (Use the normal approximation.)
(a)
How many deposits should the admissions counselor accept? (Round your answer up to the nearest integer.)
(b)
If applicants in the number determined in part (a) are accepted, what is the probability that the freshman class size will be less than 1,045? (Round your answer to four decimal places.)
In: Statistics and Probability