Assume a binomial probability distribution has p = 0.70 and n = 300. (a) What are the mean and standard deviation? (Round your answers to two decimal places.) mean Incorrect: Your answer is incorrect. standard deviation Incorrect: Your answer is incorrect. (b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. Yes, because np ≥ 5 and n(1 − p) ≥ 5. Yes, because n ≥ 30. No, because np < 5 and n(1 − p) < 5. Yes, because np < 5 and n(1 − p) < 5. No, because np ≥ 5 and n(1 − p) ≥ 5. Correct: Your answer is correct. (c) What is the probability of 190 to 200 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (d) What is the probability of 220 or more successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (e) What is the advantage of using the normal probability distribution to approximate the binomial probabilities? The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations more accurate. The advantage would be that using the the normal probability distribution to approximate the binomial probabilities reduces the number of calculations. The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations less accurate. The advantage would be that using the normal probability distribution to approximate the binomial probabilities increases the number of calculations. Correct: Your answer is correct. How would you calculate the probability in part (d) using the binomial distribution. (Use f(x) to denote the binomial probability function.) P(x ≥ 220) = f(0) + f(1) + + f(219) + f(220) P(x ≥ 220) = f(220) + f(221) + f(222) + f(223) + + f(300) P(x ≥ 220) = f(221) + f(222) + f(223) + f(224) + + f(300) P(x ≥ 220) = 1 − f(219) − f(220) − f(221) − f(222) − − f(300) P(x ≥ 220) = f(0) + f(1) + + f(218) + f(219) Correct: Your answer is correct.
In: Statistics and Probability
Question 1:In the layout of a printed circuit board for an electronic product, there are 12 different locations that can accomodate chips. (a) If Five different types of chips are to be placed on the board, how many different layouts are possible? (b) What is the probability that five chips that are placed on the board are of the same type? Question 2: A Web ad can be designed from 4 different colors, 3 font types, 5 font sizes, 3 images, and 5 text phrases. A specific design is randomly generated by the Web server when you visit the site. Let A denote the event that the design color is red and let B denote the event that the font size is not the smallest one. Find P(A ∪ B0 ) and P(B|A). Question 3: A batch of 500 containers for frozen orange juice contains 10 defective containers. Three are selected randomly without replacement from the batch. (a) What is the probability that the second one is defective given that the third one is defective? (b) What is the probability that the third one is defective? (c) What is the probability that the first one is defective given that the other ones are not defective? Question 4: A player of a video game is confronted with a series of 4 opponents and an 80% probability of defeating each opponent. Assume that the results are independent (and that when the player is defeated by an opponent the game ends). (a) What is the probability that a player defeats all 4 opponents in a game? (b) If the game is played 4 times, what is the probability that the player defeats all 4 opponents at most twice. Question 5: A credit card contains 16 digits. It also contains a month and year of expiration. Suppose there are one million credit card holders with unique numbers. A hacker randomly selects a 16-digit credit card number. (a) What is the probability that it doesn’t belong to a real user? (b) Suppose a hacker has a 10% chance of correctly guessing the month 2 of the expiry and randomly selects a year from 2018 to 2025. What is the probability that the hacker correctly selects the month and year of expiration (all the years are equally likely)? Question 6: An optical inspection system is to distinguish among different parts. The probability of a correct classification of any part is 98%. Suppose that 3 parts are inspected and that the classifications are independent. Let the random variable X denote the number of parts that are correctly classified. (a) Determine the probability mass function X. (b) Find P(X ≤ 2)
In: Statistics and Probability
For 300 trading days, the daily closing price of a stock (in $) is well modeled by a Normal model with mean $196.55 and standard deviation $7.17. According to this model, what cutoff value of price would separate the
a) lowest 17% of the days?
b) highest 0.78%?
c) middle 61%?
d) highest 50%?
In: Statistics and Probability
For 300 trading days, the daily closing price of a stock (in $) is well modeled by a Normal model with mean $196.59
and standard deviation $7.16.
According to this model, what cutoff value of price would separate the
a) lowest 14% of the days?
b) highest 0.42%?
c) middle 63%?
d) highest 50%?
In: Statistics and Probability
For 300 trading days, the daily closing price of a stock (in $) is well modeled by a Normal model with mean $195.61 and standard deviation $7.15. According to this model, what cutoff value of price would separate the
a) lowest 11% of the days?
b) highest 0.86%?
c) middle 58%?
d) highest 50%?
In: Statistics and Probability
usign the literature value of the acetic acid aand answer the following questions
pKa for acetic acid=4.74 , pH=4.35
Group#1: Buffer pH = 4.00
Group#2: Buffer pH = 4.35
Group#3: Buffer pH = 4.70
Group#4: Buffer pH = 5.00
Group#5: Buffer pH = 5.30
Group#6: Buffer pH = 5.60
1. Explain which group should havethe BEST OPTIMAL BUFFER (see choices above).
2. Explain which group has a buffer that has the HIGHEST BUFFERING CAPACITY AGAINST NaOH.
3. Explain which group has a buffer that has the HIGHEST BUFFERING CAPACITY AGAINST HCl.
4. Is the best optimal buffer the same as the buffer that has the HIGHEST buffer capacity againstNaOH? Explain your reasoning.
5. Is the best optimal buffer the same as the buffer that has the HIGHEST buffer capacity against HCl? Explain your reasoning.
In: Chemistry
At one point, A well known Restaurant chain sold cherry pies. A stats prof enlisted the help of one of his classes to gather data on the number of cherries per pie.
0,1,2,1,1,2,3,1,1,0,1,4,0,1,1,0,1,1,2,2,1,0,0,2,1,3,2,1,0,0,1,0,0,2,4
Assuming that, for cherry pies sold by the restaurant, the number of cherries per pie has A poisson distribution with the mean from part A, obtain the probability distribution of the number of cherries per pie. Let X denote the number of cherries in A pie.
X P(X=x
8 |
In: Statistics and Probability
Many students brag that they have more than 150 friends on a social media website. For a class project, a group of students asked a random sample of 13 students at their college who used the social media website about their number of friends and got the data available below. Is there strong evidence that the mean number of friends for the student population at the college who use the social media website is larger than 150?
data: 125 50 105 120 210 200 200 200 100 185 255 250 235
Complete parts a through d below.
a. Identify the relevant variable and parameter.What is the relevant variable?
What is the parameter?
b. State the null and alternative hypotheses.
c. Find and interpret the test statistic value.(Round to two decimal places as needed.)
What does the test statistic value represent?
A.The test statistic value is the number of standard errors from the null hypothesis value to the sample mean.
B.The test statistic value is the number of standard deviations from the null hypothesis value to the sample mean.
C.The test statistic value is the difference between the sample mean and the null hypothesis value.
D.The test statistic value is the expected mean of the differences between the sample data and the null hypothesis value.
d. Report and interpret the P-value and state the conclusion in context. Use a significance level of 0.05(Round to three decimal places as needed.)
What does the P-value represent?
A.The P-value is the probability of observing a sample mean this high or higher if the null hypothesis is true.
B.The P-value is the probability of observing this value for the sample mean if the null hypothesis is true.
C.The P-value is the probability of observing a sample mean this low or lower if the null hypothesis is true.
D.The P-value is the probability of the null hypothesis being true.
Since the P-value is ----- than the level of significance, the sample ------ provide evidence to reject the null hypothesis. There is ------ evidence to conclude that the mean number of friends on the social media website is larger than 150.
In: Statistics and Probability
Problem 2 ( 1 ____( solve_R__RStudio )
A particle measurement system in Shandong, China measures the count of particles less than 10 microns in diameter (PM10). It produces daily averages. It measures PM10 levels in the “alert” range of between 150 to 250 mg/m3 a number of times during the last 50 days – listed in the data sheet as “past alerts=9”. Predict the probability of the number of “future alerts” in the next 30 days, predicted alerts = 5
future alerts" = "predicted alerts".
Problem 5 ( 1 ____( solve_R__RStudio ))
-If in problem 2 the data set was comprised of measurements every minute, do you think the procedure predicting the next 30 minutes based on the last 50 minutes would work? Why or why not? What conditions are necessary for your calculation in problem 2 to be valid?
- In 4 coin tosses the probability of getting 2 heads is 0.375. The probability of getting 1 head out of 2 tosses is 0.50. In both cases half the tosses are predicted to be heads, so why is the probability higher for 1 of 2 tosses versus 2 of 4 tosses?
-In many of the calculations above we are assuming that any time you take a sample, the statistics of the larger population do not change. But you know when you are drawing cards, if two aces have been drawn, the probability of drawing another ace is reduced. Why can we normally ignore the effect of drawing a sample on the statistics of the parent population?
In: Statistics and Probability
I.- QUESTION
Based on several studies, a company has classified, according to the possibility of discovering petroleum, the geological formations in three types: I, II and III.
The company intends to drill a well in a certain site that is assigned the probabilities of 0,35; 0, 40 and 0, 25 for the three types of formations, respectively. According to experience, it is known that oil is found in 40% of type I formations, 20% of type II formations and 30% of formations
type III.
a.What is the probability of discovering oil?
b.What is the probability of discovering oil and that the geological formation is not of type I?
c.If the company does not discover oil at that location, determine the probability that there is a type II formations.
II.-QUESTION
The average number of claims to an insurance company is 3 claims per day.
a. Find what is the probability that in a week there will be at least 5 days, 2 or 3 or 4
demands.
b. Determine the probability that in a month, at least 15 days and at most 22 days, the number of
demands is between 3 and 6 demands.
III.- QUESTION
The diameter of a dot produced by a printer can be associated with a v.a.c. normally
distributed. It is known that 97, 72% of the time its diameter is greater than 0.0012 inches and 0, 62% of the times its diameter is less than 0.001 inches. a. Find the mean and variance of the diameter of the point.
b. Find the IP that the diameter of a point is greater than 0,0026 inch.
c. Find the IP that a diameter is between 0,014 and 0, 0026 inch.
d. What is the maximum variability that will be achieved so that the IP of a diameter is between 0, 0014 and 0,0026 inches is 99,5%.?
In: Statistics and Probability