CCC Standard Deviation Questions
1. Lithium watch batteries of a certain brand are delivered to stores in batches of 100. The defective rate
in the population of such batteries is 1.5%.
(a) Calculate the mean and the standard deviation of the number of defective batteries in a randomly
selected batch.
(b) What is the probability that in a randomly selected batch there will be more than 1 defective batteries?
(c) The company incurs a loss of $8 for each defective battery. What is the expected loss per batch?
(d) Suppose now that there is an $8 loss for each defective battery, but there is a $6 reward for each batch
that has no defective batteries. Calculate the expected loss per batch.
2. A random sample of 40 station wagons and minivans sold in the USA in 2018 has been selected and the
collision-damage rating of each vehicle has been recorded. In this sample the average rating is 75 points(the
maximal possible rating is 100), and the sample standard deviation is 11.5 points. Create a 95% confidence
interval for the average rating of all wagons and minivans sold in the USA in 2018.
3. The objective of a study has been to decide whether consumers consider more price or quality. In a poll
of 2,000 American adults, 64% claimed that they mainly base their buying decisions on price.
(a) Construct a 99% confidence interval for the percentage of American adults who base their buying
decisions more on price than quality.
(b) Suppose that you decrease the confidence level from 99% to a smaller probability. How would the left
endpoint change ( increase or decrease)? How would the right endpoint change (increase or decrease)?
4. In a survey for a future election a random sample of size 100 has been selected. Within that sample 8%
said that they will vote candidate A.
(a) Test the hypothesis that candidate A will receive more than 6% of the vote in the election. Make
the alternative hypothesis that the proportion of votes candidate A will receive is more than 6%. Use 5%
significance level.
(b) Calculate the p-value of the above test.
(c) What would be your decision if in question (a) the significance level had been 1%?
5. It has been determined that the population average household income in a county is µ = 80, 000, and the
population standard deviation σ = 7, 000. Let X¯ be the average income in a random sample of 60 households
from that county.
(a) What is the mean and the standard deviation of X¯?
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(b) Find the probability that X¯ will be larger than 82,000.
(c) What is the probability that the total income in the sample of 60 is less than 4,740,000?
6. The US Food and Drug Administration wants to estimate the proportion of the US population having
diabetes with a 99% confidence interval. They want the width of the confidence interval (the difference
between the right endpoint and the left endpoint) to be no more than 0.02. Determine the necessary sample
size in order to achieve this objective. Assume that they have no initial information for the true population
proportion prior to the study.
7. In a casino there is a roulette wheel with 18 black slots, 18 red slots, and 2 slots without color (these are
called zero and double zero). If a player puts k dollars on red, and the ball stops in one of the red slots,
then the player receives back the k dollars she put on the table, plus an additional k dollars (so, in effect,
she wins k dollars). If the ball stops in a black slot or in a slot without color, then she loses the k dollars
she placed on the table. Player A follows a doubling strategy: first she bets $1 on red, if she loses she bets
$2 on red, if she loses again she bets $4 on red, etc. She quits the first time the ball stops in a red slot, or
when she loses all her money, whichever happens first. Initially she has 63 dollars. Calculate the expected
loss of player A.
