Author Archives: selimhasagasioglu

Producer of high-quality plastic model kits, Hanagawa, strategized a mailing campaign. Hanagawa will send informational and promotional emails to its customers. Through pilot tests, Hanagawa found out that 15% of these emails are considered spam by the customers’ emailing services.

Hanagawa knows that each such email goes through a spam filter and only if the filter clears the email, it goes to the inbox of the customers. Otherwise, it will wind up in the customer’s Spam folder. Hanagawa estimates that 45% of the spam messages and 95% of non-spam messages end up in customers’ inboxes.

1.What is the probability that the next email sent by Hanagawa winds up in a customer’s inbox?

2.What is the probability that Hanagawa’s next email is spam and ends up in a customer’s inbox?

3.What is the probability that Hanagawa’s next email is labelled as either spam or ends up in a customer’s inbox?

4.Suppose the next email sent by Hanagawa is labelled as spam. What is the probability that it ends up in a customer’s spam folder?

5.Suppose the next email sent by Hanagawa goes to a customer’s Spam folder. What is the probability that it is spam?

Arkham is a prominent action figure manufacturer known for its high-quality action figures and playsets commanding higher prices than is usual in this particular market.

Arkham is considering launching a new brand of action figures called BATS. The marketing department of Arkham is required to come up with an estimate of the average preferred price within the entire action figure market to price this brand new line viably.

The marketers randomly sampled 50 people in the action figure market. The population, i.e. the entire action figure market, is large enough and the finite population correction factor can be ignored. The standard deviation of the preferred price within the entire action figure market is estimated to be $200 (valid for questions from 1 to 6 below).

1. What is the distribution of sample means? Explain your rationale.
2. Are you required to know the distribution for the entire action figure market?
3. What is the expected value of x ̅ (x bar)?
4. Calculate the standard deviation of x ̅ (x bar).
5. The average preferred price for the sample you collected was $750. Construct the 95% confidence interval for the average preferred price for people in the entire action figure market. Similarly construct the 99% confidence interval. Why is one confidence interval bigger than the other?
6. Instead of a sample size of 50 people, you randomly sampled 130 people and the average preferred price of this sample stayed constant at $750. Construct the 95% and the 99% confidence intervals for the preferred price for people in the entire action figure market.

Now, for the questions asked below, assume that you do not know the standard deviation of the preferred price for people in the entire action figure market. The average preferred price for the sample collected remains to be the same at $750 and the standard deviation for this same sample is $200. The sample size is 50 people.

7. Estimate the distribution of the sample means.
8. Estimate the standard deviation of the preferred price for people in the entire action figure market.
9. Calculate the standard deviation of x ̅ (x bar).
10. Construct the 95% confidence interval for the average preferred price for people in the entire action figure market. Similarly construct the 99% confidence interval. Compare your findings here with those you calculated in question 5.
11. Instead of a sample size of 50 people, you randomly sampled 130 people and the average preferred price of this sample stayed constant at $750 and the standard deviation of this sample remains to be the same at $200. Construct the 95% and the 99% confidence intervals for the preferred price for people in the entire action figure market. Compare these values with those that were found in question 6.

Data Analytics and Forensics: Coroner’s Inquest

Given the family’s demographics, the probability that the family’s first child dies of SIDS is 1 out of 1300.

Considering all other factors such as the mental state of the family and the neighborhood the family lives in, the probability that the first child is murdered is 1 out of 21,700.

Unfortunately, the family’s second child also died after 18 months had passed since first child’s death. The probability that second child dies of SIDS given that first child already died of SIDS is 1 out of 130. Furthermore, the probability that second child is murdered given that the first child was murdered is 176 out of 21,700.

A coroner assigned to this case is investigating how this could happen. The first thing she wants to look at is the probability that both first child and the second child die of SIDS given the subsequent deaths of two children. Help the coroner find out this probability.

You opened the first sushi restaurant in Konoha, Hanamichi Robot Sushi, which is fully operated by robots.

The time to serve a customer is normally distributed with a mean of 8 minutes and a standard deviation of 2 minutes.

1.Find the probability that it takes 8 minutes or less to serve the next customer.

2.Find the probability that it takes 10 minutes or more to serve the next customer.

3.Find the probability that it takes 6 minutes or less to serve the next customer.

4.Do your answers to 2 and 3 resemble or differ from each other? Compare your answers.

As the owner of Hanamichi, you plan to conduct a customer survey. You will talk to 10 customers randomly entering the restaurant and try to determine how satisfied they are with your restaurant. You estimate this measure to have a binomial distribution and the probability that a guest will be satisfied is 85%.

5. Calculate the probability of the number of successes, i.e. the number of guests that will inform you that they are satisfied and create a plot demonstrating these probabilities.

6. What is the probability that 8 or more of the 10 guests with whom you speak will be satisfied?

7. What is the probability that fewer than 8 of the 10 guests with whom you speak will be satisfied?

Kyoto Games decided to work with Selim Hasagasioglu Consulting on the launch of its new hybrid gaming console.

The consultancy firm needs to determine whether the customers Kyoto Games is targeting have a different average price preference from that of the overall market.

The consulting firm randomly samples 45 people from the Kyoto Games’ target market. It is known that the mean hardware price for the overall console market is $500 and the standard deviation is $125.

1.Estimate the distribution of the sample means, explaining your rationale.

2.Do you need to know the distribution of the pricing with respect to overall hardware market and with respect to the sample means?

3.What is the expected value and the standard deviation of the sample mean, which is the standard error? Assume that population is so large that you can ignore the finite population correction factor.

4.Assume that the average price for your sample is $465. What is the probability of getting this value or lower if the target market and overall market have the same price preferences?

5.Assume that the average price for your sample is $540. What is the probability of getting this value or higher if the target market and overall market have the same average price preference?

6.Assume that your sample size is actually 120 people and the average price for the sample remains to be $540. What is the probability of getting this value or higher if the target market and overall market have the same average price preference?

7.Your sample size is 250 people and the average price for the sample stays at $540. What is the probability of getting this value or higher if the target market and overall market have the same average price preference?

Based on the mother’s demographics, the probability of a baby having a very rare disease called ‘Rare Disease’ is 0.01.

Prenatal test for the Rare Disease is 98% accurate when the baby has the disease and when the baby does not have the disease.

The mother is tested and the test is positive.

Calculate the probability that the baby does not have the disease given that the test is positive.

One of the building blocks of data analytics: Probability in the Context of Business (Medium)

The probability that a customer buys your streaming service, Halo, is 30%.

The probability that a customer buys your streaming service Halo and signs up for your company’s specific loyalty program is 20%. Every other streaming service offers loyalty program.

Loyalty programs differ among service providers. In order to sign up for the loyalty program, a customer must purchase the streaming service first.

a) Given that a customer buys your streaming service, what is the probability that the customer also signs up for your company’s loyalty program?

b) What is the probability that all customers using all kinds of streaming services also sign up for the loyalty programs of these companies if signing up for the loyalty program is independent of the streaming service they subscribed to?

PS: Current AI tools could not solve this problem.

On this planet, understanding the nature of a random experiment solves more than half of the problem at hand.

However, this may be a hard task in some particular circumstances and boundaries are blurred.

How many businesses went bankrupt in the past hour is a discrete variable you can count without trying to predict anything.

How many e-commerce companies will record positive operational cash flows next year may be relatively well predicted through a continuous distribution model.

We live in a world that is more continuous than is discrete. In this article, I expand on this fact, which alone requires everyone involved in the world of business (basically almost everyone living on earth) to know, understand, and use statistics and its tools.