Probability Distributions
A variable whose value is determined by the outcome of a random experiment
What is a random variable?
The probability that a person has a tattoo is 0.3. Find the mean and standard deviation of those who have a tattoo in a sample of size 21. Round to 3 decimal places.
What are 6.3 and 2.1?
The area to the left of z = 1.50 is
What is 0.9332?
Suppose the current annual salary of all teachers in the United States have a normal distribution with a mean of 51000 dollars and a standard deviation of 6000 dollars. Find the probability that the annual salary of a randomly selected teacher would be between 42000 and 65000 to four decimal places.
What is 0.9234?
Find the z-value if the area to the left of z is 0.6522. Round to two decimal places.
What is 0.39?
There are 15 students in a class. Let X be the number of students who show up to class on a given day. What are the possible values of X?
What are the values 0 through 15?
Thirty percent of students at a large university are known to be short-sighted. If twenty students are picked at random, find the probability that at most two of them are shortsighted. Round to 4 decimal places.
What is 0.0355?
Find P( z > -1.85).
What is 0.9678?
Most graduate schools of business require applicants for admission to take the Graduate ManagementAdmission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. What is the probability of an individual scoring above 500 on the GMAT? Round to four decimal places.
What is 0.5953?
Find x if the area to the right of x under the normal curve with a mean of 250 and standard deviation of 50 is 0.3575. Round to two decimal places.
What is 268.26?
Is the weight of newborn babies at a hospital on a given day discrete or continuous variable?
What is a continuous variable?
A farmer plants 12 saplings. On average, 15% of saplings planted fail to survive their first winter. Find the probability that more than one of his saplings will die in that first winter. Round to 4 decimal places.
What is 0.5565?
Let x be a continuous random variable that follows a normal distribution with a mean of 125.4 and a standard deviation of 19.5. Round to four decimal places the following:
the probability that x is between 72.7 and 95.3.
What is 0.0579?
The life span of scientific calculator has a normal distribution with a mean of 58 months and a standard deviation of 10 months. The company gives a warranty of 36 months to replace any defective calculator with a new one. That is any calculator that breaks within 36 months of purchase will be replaced. Find the percentage of calculators that would need to be replaced. Round to two decimal places.
What is 1.39% ?
Find z if the area to the right of z under the standard normal curve is 0.7550. Round to two decimal places.
What is - 0.69 ?
Is the number of students in classroom a discrete or continuous random variable?
What is a discrete random variable?
At Covington High School, 20% of sixth-form mathematics students retake their C1 module. There are 15 students in Mr. Smither’s class; find the probability that precisely four of them retake this module. Round to 4 decimal places.
What is 0.1876?
Let x be a continuous random variable that follows a normal distribution with a mean of 125.4 and a standard deviation of 19.5. Round to four decimal places the following:
the probability that x is greater than 132
What is 0.3675?
The shelf life of a particular cheese is normally distributed with a mean of 12 days and a standard deviation of 3 days. About what percent of the cheese last between 10 and 15 days? Round to two decimal places.
What is 58.89% ?
Find x if a normal curve has a mean of 34 and a standard deviation of 4. The area from x to the mean is 0.1754 and x is less than the mean. Round to two decimal places.
What is 32.18?
A probability distribution lists all the possible values of a random variable and their corresponding probabilities.
Each probability for X must be between ____ and ____.
The sum of all probabilities must equal ____.
What are 0 and 1 and 1?
There were ten green bottles sitting on the wall. The probability of a green bottle accidentally falling is 0.95. What is the probability that fewer than 8 of the green bottles accidentally fall? Round to 4 decimal places.
What is 0.0115?
Find P(0 < z < 2.33).
What is 0.4901?
A line up for tickets to a local concert had a mean waiting time of 20 min with a standard deviation of 4 min. What percentage of the people in line waited for more than 28 minutes? Round to two decimal places.
What is 2.28 % ?
Most graduate schools of business require applicants for admission to take the Graduate Management
Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with amean of 527 and a standard deviation of 112. How high must an individual score on the GMAT in order to score in the highest 5%? Round to the nearest whole number.
What is 711?