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2 answers:
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Answer:
a) Therefore 92.64% of customers receive the service for half-price.
b) Therefore it would take 8.52 minutes
Step-by-step explanation:
Given that ime required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution with:
mean (μ) = 15 minutes
Standard deviation (σ) = 3.5 minutes
a) The z score is given by the equation:
Since the service will take no longer than 20 minutes,
Using the probability table to get the probability of the z score
percent of customers receive the service for half-price = P(X < 20) = P(z < 1.43) = 0.9236 = 92.64%
Therefore 92.64% of customers receive the service for half-price.
b) Since the probability is 3% = 0.03, this corresponds with a z score of -1.88
Therefore:
Therefore it would take 8.52 minutes
Step-by-step explanation:
1.) The average nightly ticket sales can be calculated as
Average sales = Average no. of customers per night x Charge per ticket
For the second night, we have
$1750 = (N)($7)
This gives us N = 250.
So, the average number of customers decreased as a result of the price increase.
To calculate the percentage change, we use the following formula:
% change =
We have -17% change in the average number of customers the theater has each night. The negative sign indicates a decrease in the number, which is consistent with our calculations.
2.) % change in prices =
Therefore, we have 40% change in the cost of ticket per person, which reflects an increase in the prices.
3.) Elasticity of Demand =
Hence, we have = -0.425
This stands consistent with the Law of Demand - as the price increases, the quantity demanded decreases.
4.) Market price is obtained by looking for a point where the quantity supplied equals the quantity demanded. From the table we see that at $75 price, there is a demand for 45,000 units of that product in that market, which the suppliers are willing to supply. Hence, that defines the market price for that product.