1. Use the following to answer 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?

2. 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.

3. 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?

Solution Summary

The solution provides step by step method for the calculation of binomial and normal probabilities. Formula for the calculation and Interpretations of the results are also included.

Find the indicated probabilities.
a. P (z > -0.89)
b. P (0.45 < z < 2.15)
Write the binomial probability as a normal probability using the continuity correction.
Binomial Probability Normal Probability
c. P ( x ≤ 56) P ( x < ? )
d. P ( x = 69 ) P ( ? < x < ?

Answer the following:
(A) Find the binomial probability P(x = 6), where n = 15 and p = 0.60.
(B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 6) in part A? Please show how you would calculate

h-p is said to be the leading seller of pc's in the U.S WITH 27% share of the pc market. if a researcher selects 130 recent pc purchases, use the normal approximation to the binomial to find the probability that more than 39 bought a h-p computer

Nathan wants to approximate a binomial probability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95.
Can Nathan use the normal curve area to approximate a binomial probability?

The probability that an appliance is in repair is .6. If an apartment complex has 100 such appliances, what is the probability that at least 70 will be in repair? Using the normal approximation to the binomial.

Nathan wants to approximate a binomial probability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95
Can Nathan use the normal curve area to approximate a binomial probability?

Consider a binomial distribution with 15 identical trials, and a probability of success of 0.5.
Find the probability that x = 2 using the binomial tables.
Use the normal approximation to find the probability that x = 2

Answer the following:
(A) Find the binomial probability P(x = 4), where n = 12 and p = 0.50.
(B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 4) in part A? Please show how you would calculate

A machine cuts circular filters from large rolls of material. If 7.3% of the filters fail to meet specifications, use the normal approximation to the binomial to compute the probability that a sample of 100 of the filters will contain 5 or fewer that fail to meet specifications.

Answer the following:
(A) Find the binomial probability P(x = 6), where n = 15 and p = 0.60.
(B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation.