Given that z is astandardnormal random variable find the

Question

1. Given that z is astandardNormal random variable, find the following probabilities:
   1. P(z <0.52)
   2. P(z > -0.63)
   3. P(-0.31
2. Given that z is a standard Normal random variable, find z for each situation:
   1. the area to the left of z is 0.76
   2. the area to the right of z is 0.65
   3. the total area to the left of -z and to the right of z is 0.1
3. Given that x is a Normal random variable with mean 5 and standard deviation 2, find the following probabilities:
   1. P(x <6.5)
   2. P(x >7.5)
   3. P(3.5
   4. P(6.5
4. Given that x is a Normal random variable with mean 10 and standard deviation of 2.5, find x for each situation:
   1. the area to the left of x is 0.05
   2. the area to the left of x is 0.65
   3. the area to the right of x is 0.45
   4. the area to the right of x is 0.975
5. Waiting times at ABC Bank's teller line follow a Normal distribution with an average of 5 minutes. If the standard deviation of the distribution is 2.5 minutes, answer the following questions:
   1. What is the probability that the waiting time is longer than 8.5 minutes?
   2. What is the probability that the waiting time is shorter than 4 minutes?
   3. What is the probability that the waiting time is between 3 to 10 minutes?
   4. 80% of customers at this teller line have to wait for at least how many minutes?
6. Scores for an IQ test are constructed by psychologists in such a way that they follow a normal distribution with mean 100 and standard deviation of 15. What score must a person have if he or she is considered a genius, i.e., his/her IQ score is within the upper 2% of the population?
7. The length of outbound calls at XYZ Inc.'s call centre follows a normal distribution. The average length is 8.6 minutes and the standard deviation is 4 minutes.
   1. If an outbound call is randomly selected, what is the probability that its length will be shorter than 7 minutes?
   2. What percentage of outbound calls will be between 9 and 12 minutes?
   3. 20% of the outbound call will be shorter than how many minutes?
8. The processing time for an incoming delivery at ABC Inc.'s warehouse follows an exponential distribution. The average processing time is 12.5 minutes.
   1. What is the probability that an incoming delivery takes less than 10 minutes to process?
   2. What percent of deliveries will take between 10 to 15 minutes to process?
9. A Pizza chain is studying its take-out and delivery operation in a market it just entered. Data collected from the study shows that the time required to get an order ready for delivery follows an exponential distribution with an average of 14 minutes.
   1. What is the probability that a randomly-selected order will be ready within 12 minutes?
   2. If the chain advertises that take-out orders will be ready for pick-up in 18 minutes or less, what percentage of orders will not satisfy this promise?