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16 Statistics Questions

1.A baseball player has a batting average of 0.275. What is the probability that he
has exactly 5 hits in his next 7 at bats?
The probability is
2. When dragons on planet Pern lay eggs, the eggs are either green or yellow. The
biologists have observed over the years that 27% of the eggs are yellow, and the
rest green. Next spring the lead scientist has permission to randomly select 64 of
the dragon eggs to incubate. Consider all the possible samples of 64 dragon eggs.
What is the mean number of yellow eggs in samples of 64 eggs? (That is the same as
asking for the expected value of the number of yellow eggs)
(Give answer correct to at least one decimal place.)
mean =
What is the standard deviation in the number of yellow eggs in samples of size 64?
(Give answer correct to at least one decimal place.)
standard deviation =
What is the variance in the number of yellow eggs in samples of size 64?
(Remember to calculate the answer using at least 5 decimal places, then give answer correct
to at least one decimal place.)
variance =
3. According to Masterfoods, the company that manufactures M&MÃ¢â‚¬â„¢s, 12% of
peanut M&MÃ¢â‚¬â„¢s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are
orange and 15% are green. You randomly select five peanut M&MÃ¢â‚¬â„¢s from an
extra-large bag of the candies. (Round all probabilities below to four decimal
places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)
Compute the probability that exactly three of the five M&MÃ¢â‚¬â„¢s are yellow.
Compute the probability that three or four of the five M&MÃ¢â‚¬â„¢s are yellow.
Compute the probability that at most three of the five M&MÃ¢â‚¬â„¢s are yellow.
Compute the probability that at least three of the five M&MÃ¢â‚¬â„¢s are yellow.
If you repeatedly select random samples of five peanut M&MÃ¢â‚¬â„¢s, on average how many
do you expect to be yellow? (Round your answer to two decimal places.)
yellow M&MÃ¢â‚¬â„¢s
yellow M&MÃ¢â‚¬â„¢s
4. Assume that a procedure yields a binomial distribution
with n=325n=325 trials and the probability of success for one trial is p=p=9/20.
Find the mean for this binomial distribution.
ÃŽÂ¼=ÃŽÂ¼=
Find the standard deviation for this distribution.
ÃÆ’=ÃÆ’=
Use the range rule of thumb to find the minimum usual value ÃŽÂ¼-2ÃÆ’ and the maximum
usual value ÃŽÂ¼+2ÃÆ’.
Enter answer as an interval using square-brackets only with whole numbers.
usual values =
5. You measure 45 turtles’ weights, and find they have a mean weight of 51
ounces. Assume the population standard deviation is 7.7 ounces. Based on this,
construct a 90% confidence interval for the true population mean turtle weight.
6. Assume that a sample is used to estimate a population mean ÃŽÂ¼ÃŽÂ¼. Find the
margin of error M.E. that corresponds to a sample of size 13 with a mean of 85.5
and a standard deviation of 19.3 at a confidence level of 99%.
Report ME accurate to one decimal place because the sample statistics are presented
with this accuracy.
M.E. =
Answer should be obtained without any preliminary rounding. However, the critical
value may be rounded to 3 decimal places.
7. The effectiveness of a blood-pressure drug is being investigated. An
experimenter finds that, on average, the reduction in systolic blood pressure is
44.3 for a sample of size 979 and standard deviation 20.4.
Estimate how much the drug will lower a typical patient’s systolic blood pressure (using
a 99% confidence level).
Enter your answer as a tri-linear inequality accurate to one decimal place (because the
sample statistics are reported accurate to one decimal place).
< ÃŽÂ¼ÃŽÂ¼ < 8. We wish to estimate what percent of adult residents in a certain county are parents. Out of 300 adult residents sampled, 27 had kids. Based on this, construct a 99% confidence interval for the proportion, p, of adult residents who are parents in this county. Give your answers as decimals, to three places. Purchase answer to see full attachment

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