Hyo-Jin makes bracelets and sells them on an online craft website. Last month, she sold 6 bracelets. After paying the website a
2 answers:
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Answer:
The total expected value and standard deviation of your winnings are -$0.081 and $3, respectively.
Step-by-step explanation:
In European roulette, a wheel with 37 slots is spun: 18 are red, 18 are black, and 1 is green.
Bettors can wager on either red or black. Winning on their chosen color means they double their bet, while losing means they forfeit their stake.
Define the probability for the ball landing in a red slot =
The probability of it landing in a black slot =
The probability for landing in the green slot =
Since bets are only placed on red or black,
The winning probability =
and losing probability =
=
If a gambler wins, they receive $3, and if they lose, it amounts to -$3.
The expected value of the total winnings is hence;
E(X) =
=
= = -$0.081
Furthermore, the standard deviation of the total winnings is given by;
S.D.(X) =
=
= = $9
Thus, S.D.(X) =
= = $2.99 ≈ $3
Consequently, the anticipated value and standard deviation of your total winnings are -$0.081 and $3, respectively.
Answer:
A) The estimated proportion of women whose platelet counts fall within 2 standard deviations of the mean, or between 118.5 and 377.3, is 95%.
B) The estimated percentage of women with platelet counts ranging from 53.8 to 442.0 is 99.7%.
Step-by-step explanation:
Provided data:
mean;μ = 247.9
standard deviation;σ = 64.7
A) We seek to find the estimated percentage of women with platelet counts within 2 standard deviations from the mean, which translates to values between 118.5 and 377.3.
Based on the attached image, the empirical curve indicates that the likelihood within 1 standard deviation of the mean is (34% + 34%) = 68%.
In contrast, the likelihood within 2 standard deviations from the mean is (13.5% + 34% + 34% + 13.5%) = 95%
Therefore, the estimated percentage of women having platelet counts within 2 standard deviations of the mean, or ranging from 118.5 to 377.3, equals 95%
B) Next, we want to determine the estimated percentage of women with platelet counts between 53.8 and 442.0.
The values of 53.8 and 442.0 correspond to 3 standard deviations from the mean.
Let’s verify that.
Since mean;μ = 247.9
standard deviation;σ = 64.7;
μ = 247.9
σ = 64.7
μ + 3σ = 247.9 + 3(64.7) = 442
Also;
μ - 3σ = 247.9 - 3(64.7) = 53.8
From the attached empirical curve, it can be seen that at 3 standard deviations from the mean, the probability percentage is;
(2.35% + 13.5% + 34% + 34% + 13.5% + 2.35%) = 99.7%
