Exam 6: Continuous Distributions

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 height of the rectangle depicting a uniform distribution is the probability of each outcome and it is the same for all of the possible outcomes.

Based on the caterer's experience, 38% of attendees to events will prefer chicken for the main dish.As the caterer plans for an event attended by 780 individuals, the normal approximation will be used for the binomial with a correction for continuity.In this case, what is the standard deviation of the number that she would expect to prefer chicken, when determining the probability that less than 300 will prefer chicken?

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

Within a range of z scores from -2 to +2, you can expect to find ___ per cent of the values in a normal distribution.

Let z be a normal random variable with mean ( $\mu$ )0 and standard deviation ( $\sigma$ )of 1.What is P(z > 2.4)?

The average time between phone calls arriving at a call centre is 30 seconds.Assuming that the time between calls is exponentially distributed, find the probability that more than a minute elapses between calls.

Based on the caterer's experience, 38% of attendees to events will prefer chicken for their main dish.As the caterer plans for an event attended by 780 individuals, the normal approximation will be used for the binomial with a correction for continuity.In this case, what is the average number the caterer would expect to prefer chicken, when determining the probability that less than 300 will prefer chicken?

A normal distribution with a mean of zero and a standard deviation of 1 is called a null distribution.

The mean of an exponential distribution is equal to 1/λ.

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

If x, the time (in minutes)to complete an change job at a 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 ___.

The expected (mean)life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.The life of this bulb is normally distributed.What is the probability that a randomly selected bulb would last longer than 1,150 hours?

Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 kilometres and a standard deviation of 5000 kilometres.What is the probability that a randomly selected tire of this brand has a life of at most 30,000 kilometres?

The normal distribution is an example of ___.

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

The probability that someone will prefer Coke over Pepsi is 0.56.A researcher asked 90 people which soda pop they preferred, and used the normal approximation to the binomial with a correction for continuity, what would be the standard deviation used in the calculation?

If x is uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then the standard deviation of this distribution is approximately___.

The expected (mean)life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.The life of this bulb is normally distributed.What is the probability that a randomly selected bulb would last fewer than 940 hours?

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.