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University of California Davis

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1. A surfboard company is famous for making long boards. The resale price of their
used surfboards is a normally distributed variable with a mean of \$1,500 and a
standard deviation of \$300.
(round each answer to 2 decimal places)
a. What's the probability of a randomly selected tree being worth between \$1,800 and
\$2,100?
Z-score for \$1,800: 1.00
Z-score for \$2,100: 2.00
Prob (\$1,500<x<\$1,800): 0.34
Prob (\$1,500<x<\$2,100): 0.48
Prob (\$1,800<x<\$2,100): 0.14
2. A lumbering company has secured the rights to remove trees from a tract of land.
The value of trees that are removed is a normally distributed variable with a mean of
\$500 and standard deviation of \$100. A group of 4 trees is selected at random. What
is the probability that the average value of these trees is over \$600?
(round each answer to two decimal places)
Sampling Mean: 500
Sampling Standard Deviation: 50
Z-score for \$600: 2.00
Prob (\$500<x<\$600): 0.48
Prob (\$600<x): 0.02
3. 160 randomly selected voters were surveyed. 120 of the voters said they would vote
“yes” on Proposition O, a local city bond act. Construct a 95% confidence interval for
the true proportion of all registered voters who will vote “yes”.
a. "p-hat" (sample proportion): 0.75
b. α/2: 0.025
c. Zα/2: 1.96
d. Confidence Interval Minimum Value: 0.68
e. Confidence Interval Maximum Value: 0.82

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4. 160 randomly selected voters were surveyed. 120 of the voters said they would vote
“yes” on Proposition O, a local city bond act. At the 95% level test the alternate
hypothesis that the true proportion of “yes” votes will be enough for Proposition O to
pass. (assume over 50% is needed)
(Round answers to 2 decimal places as needed)
a. Alternate Hypothesis, Ha: p > 0.5
b. Critical Value for Rejection Region: 1.64
c. Test Stat: 6.32
d. Do you reject the null hypothesis? Yes
e. Why or why not? Reject because Test Stat is greater than the critical
value, and thus falls in the rejection region.
5. The table below lists summary statistics for two pitchers for a single baseball game.
Leftie McGee Rightie Tighty
Sample Mean (pitches per inning) 12.0 13.0
Sample Variance (pitches per inning) 3.5 8
Sample Size (# of innings) 9 9
Set up a 90% confidence interval for the population (entire season) variance for Rightie
Tighty's pitches per inning. (Round all answers to two decimal places)
a. Degrees of Freedom: 8
b. χ/2: 2.73
c. χ21-α/2: 15.51
d. Confidence Interval Minimum Value: 4.13
e. Confidence Interval Maximum Value: 23.42

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1. A surfboard company is famous for making long boards. The resale price of their used surfboards is a normally distributed variable with a mean of \$1,500 and a standard deviation of \$300. (round each answer to 2 decimal places) a. What's the probability of a randomly selected tree being worth between \$1,800 and \$2,100? Z-score for \$1,800: 1.00 Z-score for \$2,100: 2.00 Prob (\$1,500 Purchase document to see full attachment
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