Exam 6: Continuous Distributions

If the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140, inclusively (90 $\le$ x $\le$ 140), then the standard deviation of this distribution is approximately __________________.

Completion time (from start to finish)of a building remodelling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days.To be 99% sure that we will not be late in completing the project, we should request a completion time of ___ work-days.

The z distribution is a normal distribution with a mean of zero and a standard deviation of one.

Suppose the total time to fill a routine prescription at a local pharmacy averages 35 minutes starting from the time the physician places the order to the time it is dispensed.Assume the standard deviation is 11 minutes.A z score of -1.3 was calculated.What is the value of x?

The area to the left of the mean in any normal distribution is equal to ___.

Let z be a normal random variable with mean ( $\mu$ )0 and standard deviation ( $\sigma$ )of 1.What is P(1.3 < z < 2.3)?

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.

Suppose the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140, inclusively (90 $\le$ x $\le$ 140), then the height of this distribution, f(x), is __________________.

For an exponential distribution with a lambda (λ)equal to 4, the standard deviation is equal to ___.

Completion time (from start to finish)of a building remodelling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days.The probability that the project will be completed within 185 work-days is ___.

Suppose the total time to fill a routine prescription at a local pharmacy averages 35 minutes starting from the time the physician places the order to the time it is dispensed.Assume the standard deviation is 11 minutes.A z score of 3.4 was calculated.What is the value of x?

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 least 50,000 kilometres?

Let x be a binomial random variable with n=50 and p=.3.The probability of less than or equal to 13 successes, when using the normal approximation for binomial is most closely reflected by ________.

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 probability that less than 300 will prefer chicken?

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

The normal approximation for binomial distribution can be used when n=10 and p=1/5.

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

Let z be a normal random variable with mean 0 and standard deviation 1.The 75^th percentile of z is most closely reflected by ___.

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 _____________.

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)_________.