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Alex Mason has a wide-curving, uphill driveway leading to his garage. When there is a heavy snow, Alex hires a local carpenter, who shovels snow on the side in the winter, to shovel his driveway. The snow shoveler charges $30 to shovel the driveway. Following is a probability distribution of the number of heavy snows each winter.
Heavy Snows
Probability
1
1.12
2
0.19
3
0.24
4
0.22
5
0.13
Alex is considering the purchase of a new self-propelled snow blower for $575 that would allow him, his wife, or his children to clear the driveway after a snow. Discuss what you think Alex's decision should be and why.
The manager of the greeting card section of Harvey's department store is considering her order for a particular line of holiday cards. The cost of each box cards is $3 each box will be sold for $5 during the holiday season. After the holiday season, the cards will be sold for $2 a box. The card section manager believes that all leftover cards can be sold at that price. The estimated demand during the holiday season for the cards, with associated probabilities, is as follows:
Demand (boxes)
25
26
27
29
30
Probability
0.10
0.15
0.30
0.20
0.15
0.10
Develop the payoff table for this decision situation and compute the expected value for
each alternative and identify the best decision.
b. Compute the expected value of perfect information.
Two balls are drawn in succession without replacement from an urn containing 4 red balls and 3 black balls. Find the probability distribution of the number of black balls.
Given a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample of a. 4 has a mean between 49 and 52. b. 16 has a mean between 49 and 52. c. 25 has a mean between 49 and 52
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 50 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 3000 batteries, and 1% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
Professor Kang of Pampanga University claims that the average IQ of his students is more than 1010. A random sample of 30 students were selected to see if his claim is true. What is the null and alternative hypothesis?
Which of the following summary measures is affected most by outliers?
a.) the median
b.) the mean
c.) the range
d.) the interquartile range
e.) the all of the above
What statistical test do you use to measure an association between one nominal scaled
variable and one ordinal scaled variable?
a.) Spearman Rank Correlation
b.) Chi-square Test
c.) Regression Analysis
d.) None of the above, you can’t measure an association between variables from different
types of data.
A population consists of three numbers (3,5,9).Consider all possible samples of size n=2 which can be drawn WITHOUT REPLACEMENT from the population.
Questions to be answered:
Population mean
Population variance
Population standard deviation
Mean of the samples and mean of the sampling distribution of the means
Calculate the probability from the z-table. a. 𝑃(𝑍 > −0.45) b. 𝑃( 𝑍 < 2.10) c. 𝑃(0 < 𝑍 < 2.10) d. 𝑃(−0.45 < 𝑍 < 2.10)
