Exam 6: Continuous Distributions

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.Which most closely reflects the probability that a randomly selected bulb would last longer than 1150 hours?

If the probability of a binomial distribution was considering values that were greater than 14, then the correction for continuity would start at 13.5.

A recent market study has determined that the probability that a young adult would be willing to try a new online financial service that your company is offering is 50%.In a random sample of 10 young adults, the probability that exactly 5 will be willing to try this new service is _________, and the approximate probability (using the normal distribution is)_________.

Employees arrive at a cafeteria according to a Poisson process at an average rate of 30 employees per hour.The probability that after one employee arrives, the next one will arrive at least 3 minutes later is _________.

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

Correcting for continuity is necessary when a researcher is using a discrete distribution to estimate probabilities from a continuous distribution.

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 mean of this distribution is __________________.

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 height of this distribution, f(x), is __________________.

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

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 miles and a standard deviation of 5000 miles.Which probability most closely reflects that a randomly selected tire of this brand has a life between 30,000 and 50,000 miles?

Employees arrive at a cafeteria according to a Poisson process at an average rate of 30 employees per hour.The average waiting time between employees' arrivals is _________ minutes.

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.Which most closely reflects the probability that a randomly selected bulb would last fewer than 1100 hours?

Let x be a binomial random variable with n=50 and p=.3.If we use the normal distribution to approximate probabilities for this, a correction for continuity should be made.To find the probability of more than 15 successes, we should find _______.

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 25 to 28 minutes, inclusively, i.e., P(25 $\le$ x $\le$ 28)is __________________.

The average time between phone calls arriving at a call center is 30 seconds.Assuming that the time between calls is exponentially distributed, find the probability that less than two minutes elapse between calls.

A z-score is the number of standard deviations that a value of a random variable is above or below the mean.

Normal distribution is a symmetrical distribution with its tails extending to infinity on either side of the mean.

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

For an exponential distribution, the mean and the median are equal.

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 __________________.