Question

in a survey given to students, the following ages were recorded: 14, 15, 15, 16, 16, 16, 17, 18. what is the median age?
15
17
16
18
question 12 (3 points)
a company is deciding whether to launch a new product. the product will cost $100,000 to manufacture and market. if the product is successful, the company expects to make $200,000 in profit. the company estimates that the probability of the product being successful is 0.3. should the company launch the product based on expected values? the expected value is calculated as (probability of success × expected profit - cost of launch).
the expected profit from the product $160,000. since the expected profit is positive, the company should launch the product.
the expected profit from the product $60,000. since the expected profit is positive, the company should launch the product.
the expected profit from the product -$40,000. since the expected profit is negative, the company should not launch the product.
the expected profit from the product -$60,000. since the expected profit is negative, the company should not launch the product.
question 13 (3 points)
you want to buy some decorative storage containers for your dorm room. container a costs $20 each, requires 4 square feet of floor space, and holds 8 cubic feet of items. container b costs $30 each, requires 6 square feet of floor space, and holds 18 cubic feet of items. you have $150 to spend on storage containers. your dorm room has no more than 60 square feet of space for storage containers. which of the following constraints can be used to determine how many of each type of storage container you should buy to maximize storage volume?
20a + 30b ≤ 150
8a + 18b ≤ 60
a + b ≤ 60
4a + 6b ≤ 60

Explanation:

Question 11

Step1: Arrange data in ascending order

The data 14, 15, 15, 16, 16, 16, 17, 18 is already in ascending - order.

Step2: Find the middle value

There are \(n = 8\) data points. For \(n\) even, the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=4\) and \(\frac{n}{2}+1 = 5\). The 4th value is 16 and the 5th value is 16. Median=\(\frac{16 + 16}{2}=16\).

Step1: Use the expected - value formula

The expected - value formula is \(E = P\times\text{Profit}-\text{Cost}\), where \(P = 0.3\), \(\text{Profit}=200000\) and \(\text{Cost}=100000\).

Step2: Calculate the expected value

\(E=0.3\times200000 - 100000=60000 - 100000=- 40000\). Since the expected profit is negative, the company should not launch the product.

Step1: Analyze the cost constraint

You have a budget of $150. Container A costs $20 each and container B costs $30 each. So the cost constraint is \(20A + 30B\leq150\).

Step2: Analyze the space constraint

Your dorm room has no more than 60 square feet of space for storage containers. Container A requires 4 square feet and container B requires 6 square feet. So the space - related constraint is \(4A + 6B\leq60\).

Answer:

16

Question 12