Question

The mean temperature for the month of July in Boston, Massachusetts is 73 degrees Fahrenheit. Plot the following data, which represent the observed mean temperature in Boston over the last 20 years:

199872199969200078200170200267200374200473200565200677200771200875200968201072201177201265201379201477201578201672201774

Is this a normal distribution? Explain your reasoning.

What is an outlier? Are there any outliers in this distribution? Explain your reasoning fully.

Using the above data, what is the probability that the mean will be over 76 in any given July?

Using the above data, what is the probability that the mean will be over 80 in any given July?

A heatwave is defined as 3 or more days in a row with a high temperature over 90 degrees Fahrenheit. Given the following high temperatures recorded over a period of 20 days, what is the probability that there will be a heatwave in the next 10 days?

Day 193Day 288Day 391Day 486Day 592Day 691Day 790Day 888Day 985Day 1091Day 1184Day 1286Day 1385Day 1490Day 1592Day 1689Day 1788Day 1890Day 1988Day 2090

Customer surveys reveal that 40% of customers purchase products online versus in the physical store location. Suppose that this business makes 12 sales in a given day

Does this situation fit the parameters for a binomial distribution? Explain why or why not?

Find the probability of the 12 sales on a given day exactly 4 are made online

Find the probability of the 12 sales fewer than 6 are made online

Find the probability of the 12 sales more than 8 are made online

Your own example:

Choose a company that you have recently seen in the news because it is having some sort of problem or scandal, and complete the following:

Discuss the situation, and describe how the company could use distributions and probability statistics to learn more about how the scandal could affect its business.

If you were a business analyst for the company, what research would you want to do, and what kind of data would you want to collect to create a distribution?

Would this be a standard, binomial, or Poisson distribution? Why?

List and discuss at least 3 questions that you would want to create probabilities for (e.g., What is the chance that the company loses 10% of its customers in the next year?).

What would you hope to learn from calculating these probabilities?

Assuming that upper management does not see the value in expending the time and money necessary to collect data to analyze, make an argument (at least 100 words) convincing them that the expenditure is necessary and explaining some dangers the company could face by not knowing what the data predict.

Answer 1

Answer :

Customer survey:

As this is the binomial distribtuion that the success probability is 0.4 and out of 12 sales, alll are independant to each other, and they will have two choices, either to shop online or physical location.

As we have bivariate and independant choice it follows the binomial distribuiton:

As per the binomial distributon:

P(X =x) = ^NC_X * P^X * (1-P)^(N-X)

P(X = 4) = ¹²C₄ * 0.4⁴ * 0.6⁸

P(X = 4) = 495 * 0.0256 *0.0168

P(X = 4) = 0.2128

So probaiblity fo exact 4 sales to be online out of 12 sales is 0.2128

Fewer than 6 sales online

P(X <6) = P(X = 0) +P(X = 1) +P(X = 2) +P(X = 3) +P(X = 4) +P(X = 5)

= ¹²C₀ * 0.4⁰ * 0.6¹² +¹²C₁ * 0.4¹ * 0.6¹¹ +¹²C₂ * 0.4² * 0.6¹⁰ +¹²C₃ * 0.4³ * 0.6⁹ +¹²C₄ * 0.4⁴ * 0.6⁸ +¹²C₅ * 0.4⁵ * 0.6⁷

= 0.002176 +0.017414 +0.06385 +0.1419 +0.2128 +0.2270

= 0.6652

So probabiltiy of less than six sales to be online = 0.6652

more than 8 sales online

P(X >8) = P(X = 9) +P(X = 10) +P(X = 11) +P(X = 12)

= ¹²C₉ * 0.4⁹ * 0.6³ +¹²C₁₀ * 0.4¹⁰ * 0.6² +¹²C₁₁ * 0.4¹¹ * 0.6¹ +¹²C₁₂ * 0.4¹² * 0.6⁰

= 0.01245 +0.002491 +0.0003019 +0.00001678

= 0.01526

So probabiltiy of more than 8 sales to be online = 0.01526