In a gambling game a woman is paid $30 if she draws a jack or a queen
and $50 if she draws a king or an ace from an ordinary deck of 52 playing
cards. If she draws any other card, she loses. How much should she pay to
play if the game is fair?
The average life of a certain type of small motor is 10 years with a
standard deviation of 2 years. The manufacturer replaces free al motors
that fail while under guarantee. If he is willing to replace only 5% of the
motors that fail, how long a guarantee should he offer? Assume that the
lives of the motors follow a normal distribution.
If the standard error of the mean for the sampling distribution of random
samples of size 36 from a larger of infinite population is 2, how large must
the size of the sample become if the standard error is to be reduced to 1.2?
Three brands of batteries are under study. It is suspected that the lives (in
weeks) of the three brands are different. Five batteries of each brand are
tested with the following results:
(a) Are the mean lives of these brands of batteries different under the
same population variance assumption? Significant level α = 0.05
(Need to show ANOVA table) (10%)
(b) Construct a 95% confidence interval estimated on the mean life on
battery brand 2. (10%)
(c) What is the minimum absolute difference of sample mean life of
batteries between brand 2 and 3 if the same population variance
estimation is MES of question (a), we will conclude that the means are
different under the significant level α = 0.05 ? (10%)
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