Solve the following problems:
Q1. Use the following to response questions: The table below presents the probability distribution for X = the number of email messages you will receive in the next 10 minutes.
X 0 1 2 3
P(X) .35 .35 .25 .05
a. What is the probability that no emails will be received?
b. What is the probability that at least one email will be received?
c. What is E(X), the expected number of emails that will be received?
d. What is Var(X), the variance of the number of emails that will be received?
e. What is the Std(X), the standard deviation of the number of emails that will be received?
Q2. Site preparation for new housing developments for tracts of 50 houses are normally distributed with a mean of 200 and a standard deviation of 10 workdays.
a. Find the probability that the site is completed within 185 workdays
b. Find the probability that the site will not be completed within 215 workdays
c. Find the probability that the site is completed between 185 and 215 days.
Q3. John Rengel is the Quality Assurance Supervisor for Vino Supremo Vinyards. He knows that 10 percent of each box of corks is undersized.
a) If he were to randomly select 120 corks from the next box, then how many of these corks would John expect to be undersized?
b) If he were to randomly select 120 corks from each box, then what would John calculate as the standard error of the number of undersized corks?
c) What is the probability that John will find 15 or more corks defective in a randomly selected box?