8.3.10 Dave is playing blackjack at his local casino. He starts with $1,000 and on each hand he bets 50% of his money. If he win
2 answers:
Answer:
The amount Dave got after 3 wins and 2 loose is $843.75. The order of win and loose doesn't matter.
Step-by-step explanation:
- We are given with a word problem
- We are asked to find the amount he had after 5 hands
- We can do this in two steps
Step 1 : Identifying the percentages
Step 2 : Finding the amount left
Step 1 of 2
We are given with a word problem. He bets 50% of his money. If he wins he get his bet, if he loose he will loose the money too. If he wins he will get the money as 150%.
That is, 1.5
If he loose he will loose money by 50%
That is, 0.50
Step 2 of 2
The amount got after 5 hands with 3 wins and 2 loose is,
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Answer:
The 95% confidence interval is given by (25.71536 ;28.32464)
And if we need to round we can use the following excel code:
round(lower,2)
[1] 25.72
round(upper,2)
[1] 28.32
And the interval would be (25.72; 28.32)
Step-by-step explanation:
Notation and definitions
n=50 represent the sample size
represent the sample mean
represent the sample standard deviation
m represent the margin of error
Confidence =88% or 0.88
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Calculate the critical value tc
In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 88% of confidence, our significance level would be given by and
. The degrees of freedom are given by:
We can find the critical values in R using the following formulas:
qt(0.06,49)
[1] -1.582366
qt(1-0.06,49)
[1] 1.582366
The critical value
Calculate the margin of error (m)
The margin of error for the sample mean is given by this formula:
With R we can do this:
m=1.582366*(5.83/sqrt(50))
m
[1] 1.304639
Calculate the confidence interval
The interval for the mean is given by this formula:
And calculating the limits we got:
Using R the code is:
lower=27.02-m;lower
[1] 25.71536
upper=27.02+m;upper
[1] 28.32464
The 95% confidence interval is given by (25.71536 ;28.32464)
And if we need to round we can use the following excel code:
round(lower,2)
[1] 25.72
round(upper,2)
[1] 28.32
And the interval would be (25.72; 28.32)