Exam 6: Continuous Distributions

If x,the time (in minutes)to complete an oil change job at certain auto service station,is uniformly distributed over the interval 20 to 30,inclusively (20 $\le$ x $\le$ 30),then the standard deviation of this distribution is __________________.

For an exponential distribution,the mean is always equal to its variance.

The area under the standard normal distribution between 0 and 2 is twice the area between 0 and 1.

If arrivals at a bank followed a Poisson distribution,then the time between arrivals would follow a binomial distribution.

A standard normal distribution has the following characteristics:

The total area underneath any normal curve is equal to _______.

If x,the time (in minutes)to complete an change job at certain auto service station,is uniformly distributed over the interval 20 to 30,inclusively (20 $\le$ x $\le$ 30),then the probability that an oil change job is completed in less than 17 minutes,i.e.,P(x < 17)is __________________.

The net profit from a certain investment is normally distributed with a mean of $2,500 and a standard deviation of $1,000..The probability that the investor's net gain will be at least $2,000 is _____________.

Let z be a normal random variable with mean 0 and standard deviation 1.The 90^th percentile of z is ____________.

Suppose you are working with a data set that is normally distributed with a mean of 400 and a standard deviation of 20.Determine the value of x such that 60% of the values are greater than x.

Assuming an equal chance of a new baby being a boy or a girl (that is,p= 0.5),we would like to find the probability of 40 or more of the next 100 births at a local hospital will be boys.Using the normal approximation for binomial with a correction for continuity,we should use the z-score _______

At a certain workstation in an assembly line,the time required to assemble a component is exponentially distributed with a mean time of 10 minutes.Find the probability that a component is assembled in 3 to 7 minutes?

Participants in a 2 day biking event,cross the finish line at a rate of 10 bike riders per fifteen minute interval.The probability that less than 10 minutes will elapse between car arrivals is _____________.

If x is uniformly distributed over the interval 8 to 12,inclusively (8 $\le$ x $\le$ 12),then P(x < 7)is __________________.

For an exponential distribution with a lambda (l)equal to 20,the mean equal to _______.

If x,the time (in minutes)to complete an change job at certain auto service station,is uniformly distributed over the interval 20 to 30,inclusively (20 $\le$ x $\le$ 30),then the probability that an oil change job is completed in 21.75 to 24.25 minutes,inclusively,i.e.,P(21.75 $\le$ x $\le$ 24.25)is __________________.

Let z be a normal random variable with mean 0 and standard deviation 1.What is P(z > -1.1)?

If x is uniformly distributed over the interval 8 to 12,inclusively (8 $\le$ x $\le$ 12),then P(x $\le$ 11)is __________________.

At a certain workstation in an assembly line,the time required to assemble a component is exponentially distributed with a mean time of 10 minutes.Find the probability that a component is assembled in 7 minutes or less?

The normal distribution is an example of _______.