# stats hw 2

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__MGT 3410 Homework 2__ Spring 2022

**Random Variables and Probability Distributions**

**1**. The demand for a product of Carolina Industries varies greatly from month to month. Based on the past three years of data, the following shows the monthly demand at Carolina Industries.

__Unit Demand__ __# Months__

300 6

400 8

500 12

600 10

a. If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product?

b. What are the variance and the standard deviation for the number of units demanded?

**2**. Military Radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue the warning. Assume that a particular detection system has a 0.85 probability of detecting a missile attack. Answer the following questions using the Binomial probability distribution.

a. What is the probability that 1 detection system will detect an attack?

b. If 2 detection systems are installed in the same area and operate independently, what is the probability that at least 1 of the systems will detect the attack?

c. If 3 systems are installed, what is the probability that at least 1 of the systems will detect the attack?

d. Would you recommend that multiple detection systems be operated? Explain.

**3**. The average stock price for companies making up the S&P 500 is $30, and the standard deviation is $8.20. Assume the stock prices are normally distributed.

a. What is the probability a company will have a stock price of at least $35?

b. What is the probability a company will have a stock price no higher than $23?

c. How high does a stock price have to be to put a company in the top 5%?

**4. **The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds.

a. Write down the p.d.f.

b. What is the probability the time between vehicle arrivals is 12 seconds or less?

c. What is the probability there will be 30 or more seconds between arriving vehicles?

**Note: **Homework solution must be submitted electronically to **Homework 2 folder** in “Assignments” on D2L.

It is your choice to submit all of your work or just the final answer only. If you only submit the final answer and the answer is wrong, you will lose all the points assigned to that question. If you also show the steps how you get that answer, you still can earn partial credit as long as the steps are not completely wrong.

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