Assignment:
Show all your work here. Underline or highlight your final answer.
1. A company orders components from Japan. When the products are delivered, it must convert dollars into yen to pay the producer. When the next order is delivered, it believes the exchange rate will take on the following values with shown probabilities.
|
Exchange Rate (yen per dollar)
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Probability
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|
100
|
0.1
|
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110
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0.2
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120
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0.4
|
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130
|
0.2
|
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140
|
0.1
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a) Find the expected value of the exchange rate.
b) Find the standard deviation of the exchange rate.
c) What does the standard deviation represent?
d) Find the probability that the exchange rate will be higher than 120 yen/dollar.
2. A typical incoming phone call to your catalog sales force results in a mean order of $30 with a standard deviation of $10. You may assume a Normal distribution.
a) Find the probability that one call will result in an order of more than $35 tomorrow.
b) Consider a random sample of 25 phone calls. Find the probability that the average order will be more than $35 tomorrow.
c) Why are the probabilities computed in a) and b) different?
3. A study was conducted by your company, with 324 random interested customers indicating that they would pay an average of $18.14 for your new product. The standard deviation was $2.98.
a) Find the 95% confidence interval for the average that consumers would be willing to pay in the population.
b) Find the 99% confidence interval for the average that consumers would be willing to pay in the population.
c) Which interval (95% or 99%) is more likely to include the unknown population mean? Why?
d) Test the hypothesis that interested consumers would be willing, on average, to pay $20.00 for the new product, against the two-sided alternative. (At the 5% level of significance).
4. Active consumers make up 14.6% of the market and spend an average of $16.23 per month on your product. Passive consumers make up 24.8% of the market and spend an average of $9.85 per month. The remaining consumers have an average spending of $14.77. Find the average spending for all consumers.