Give the solution for the following questions in details
1. Suppose that the waiting time for a pizza to be delivered to an individual’s residence has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. What is the probability that a randomly selected individual will have a waiting time:
[3.5] a. Between 15 and 45 minutes?
[3.5] b. At least 10 minutes?
[3.5] c. At most 10 minutes?
[3.5] d. No more than 45 minutes?

2. The lifetime of a particular type of light bulb are approximately normally distributed with a mean of 1200 hours and a standard deviation of 140 hours.
[4] a. Find the probability that a randomly chosen bulb will burn longer than 1400 hours.
[4] b. Find the probability that a randomly chosen bulb will last between 1000 and 1050 hours.
[4] c. Twenty percent of the lightbulbs have a lifetime of less than what value?
[4] d. At what number of hours should the warranty lifetime be set so that only 2% of bulbs must be replaced under warranty?

3. Data collected over a long period of time showed that a particular genetic defect occurs in 1 of every 1000 children. Let X be the random variable “number of children with genetic defect in a sample of 50,000 children examined”. The records of a medical clinic show X = 60 children.
[4] a. What is the probability of observing a value of X equal to 60 or more?
[2] b. Would you say that the observation of X = 60 children with genetic defect was rather unlikely?

4. Suppose a random sample of n = 49 observations is selected from a population that has normal distribution with mean 106 and standard deviation 12.
_
[4] a. Give the mean and the standard deviation of the sample mean X.
_
[4] b. Find the probability that X exceeds 110.
[4] c. Find the probability that the sample mean deviates from the population mean by less than 4.

5. [7] The weight of the eggs produced by a certain breed of hen has an unknown distribution with a mean of 65 grams and a standard deviation of 5 grams. If you purchase 144 eggs, what is the approximate probability that the average weight of these eggs is less than 64 grams? Justify the use of any probability distribution you might use.

Give the solution for the following questions in details 1. Suppos...