Practice Questions on Normal Distribution1- Let X be a normally distributed random variable with mean μ = 16 and standard deviation σ =

3. Find (a) P(10 < X< 18) (b) P(16 < X< 18) (c) P(X > 14)2- for a normally distributed random variable with mean -44 and standard deviation 16, find the

probability that the value of the random variable will be (a) above 0 (b) -10 (c) below 03- A normal random variable has mean 0 and standard deviation 4. Find the probability that the

random variable will Be (a) above 2.5 (b) between 2 and 3 (c) below 14- The time it takes an international telephone operator to place an overseas phone call is

normally distributed with mean 45 seconds and standard deviation 10 seconds.5- (a) What is the probability that my call will go through in less than 1 minute?6- (b) What is the probability that my call will get through in less than 40 seconds?7- (c) What is the probability that I will have to wait more than 70 seconds for my call to go

through?8- The number of votes cast in favor of a controversial proposition is believed to be

approximately normally distributed with mean 8,000 and standard deviation 1,000. The proposition needs at least 9,322 votes in order to pass. What is the probability that the proposition will pass? (Assume numbers are on a continuous scale.)

9- A manufacturing company regularly consumes a special type of glue purchased from a foreign supplier. From past experience, the materials manager notes that the company’s demand for glue during the uncertain lead-time is normally distributed with a mean of 187.6 gallons and a standard deviation of 12.4 gallons. The company follows a policy of placing the order when the glue stock falls to a predetermined value, called “re-order point”. It the demand during lead-time exceeds the reorder level, the glue would go ‘stock-out’ and production process would have to stop. (a) If the re-order point is kept at 187.6 gallons, what is the probability that a stock-out condition would occur? (b) If the reorder point is kept at 200 gallons, what is the probability that a stock out condition would occur? (c) If the company wants to be 95% confident that the stock-out condition will not occur, what should be the reorder point? The reorder point minus the mean demand during lead-time is known as the "safety stock." What is the safety stock in this case?

10- If X is a normally distributed random variable with mean 125 and standard deviation 44, find a value x such that the probability that X will be less than x is 0.66.

11- Suppose the weights of 8000 male students are normally distributed with mean 160 ponds and standard deviation 20 pounds. Find the number of students with weights

i- Less than 100 pounds ii- Between 150 and 175 poundsiii- Greater than 155 poundsiv- Between 170 and 175 pounds v- Greater than 210 pounds

12- Suppose the weights of 1000 male students are normally distributed with mean 110 ponds and standard deviation 26 pounds. Find the number of students with weights

i- Less than 100 pounds ii- Between 130 and 155 poundsiii- Greater than 125 poundsiv- Between 120 and 155 poundsv- Greater than 178 pounds