Exam 8: Continuous Probability Distributions

Calculus Scores Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4.(Total possible points = 100. ) -{Calculus Scores Narrative} What is the probability that a randomly selected student will have a score of 94 or lower?

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. -{Subway Waiting Time Narrative} What is the probability of waiting no more than 3 minutes?

Let X represent weekly income expressed in dollars.Since there is no set upper limit,we cannot identify (and thus cannot count)all the possible values.Consequently,weekly income is regarded as a continuous random variable.

The Student t distribution with parameter v = 2 has a mean E(t)equal to:

Since there is an infinite number of values a continuous random variable can assume,the probability of each individual value is virtually 0.

A larger standard deviation of a normal distribution indicates that the distribution becomes:

Checking Accounts A bank has determined that the monthly balances of the checking accounts of its customers are normally distributed with an average balance of $1,200 and a standard deviation of $250. -{Checking Accounts Narrative} What proportion of customers have monthly balances less than $1,000?

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. -{Battery Life Narrative} What proportion of these batteries will last less than 3,600 hours?

If the random variable X is exponentially distributed,then the mean of X will be:

Which of the following distributions is not skewed?

The Student t distribution:

Suppose X has a normal distribution with mean 10 and standard deviation 2.The probability that X is less than 8 is equal to the probability that Z is less than ____________________.

If X has an exponential distribution,the possible values of X are from ____________________ to infinity.

If the parameter of an exponential distribution is 1,then which of the following is true?

Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes. -{Repair Time Narrative} What is the variance of the time it takes a technician to fix a telephone problem?

If the random variable X is exponentially distributed with parameter $\lambda$ = 0.05,then the probability P(X > 20)= 0.3679.

The shape of a c² distribution is ____________________.

We distinguish between discrete and continuous random variables by noting whether the number of possible values is countable or uncountable.

To be a legitimate probability density function,all possible values of f(x)must lie between 0 and 1 (inclusive).

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -{Electronics Test Narrative} Find the probability that a student will take no less than 55 minutes to finish the test.