The lifetime of a certain brand of an electric bulb may be considered a RV with mean 1200 h and standard deviation 250 h. Find the probability, using central limit theorem, that the average lifetime of 60 bulbs exceeds 1250 h.

Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean number of dandelions per square meter was found to be 5.3. Find the probahility of no dandelions in an area of 1m². P(x=0)= Find the probability of at least one dandelion in an area of 1m². at least one

Suppose that the speed at which cars go on the freeway is normally distributed with mean 68 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to two decimal places. If one car is randomly chosen, find the probability that is traveling less than 70 mph.

If X is a normal random variable with mean 20 and standard deviation 50. Find the probability that 15 < X < 45.

The time taken in the cycling phase of a triathlon has a mean 23.16min and standard deviation 8.39min. Find the probability that the mean cycling time taken by a random sample of 38 competitors is greater than 25 minutes. Give your answer in 3 decimal places.

Suppose that the number of customers who enter a supermarket each hour is normally distributed with a mean of 650 and a standard deviation of 230. The supermarket is open 15 hours per day. What is the probability that the total number of customers who enter the supermarket in one day is greater than 10400? (Hint: Calculate the average hourly number of customers necessary to exceed 10400 in one 15-hour day.) Probability =

If life length  ( in hours )  of certain kind of device follows chi - squared distribution with dof  10 .  Find the probability that exactly  2  of  6  such devices in a system will have to be replaced within the first  16  hours of operation. Assume that life of the devices are independent