There are 3 face cards for each of the 4 suits, leading to a total possible gain of 120, there are 40 other cards leading to a total possible loss of 80.
120 - 80 = 40.
40 / 52 (total number of cards) = about .77
Final Answer:
The expected value of a draw is positive 0.77 points.
Hope I helped :)
Answer:
The value of the annuity is $326,852.3766.
Step-by-step explanation:
Here is the required formula to find the present value of annuity:
We can find the present value of annuity:

Here:
P = $50,000
n = represents the number of number of periods
r = 0.11

PV = $326,852.3766
The value of the annuity is $326,852.3766 i.e. PV = $326,852.3766.
Keywords: discount rate, present value of annuity
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Using the normal distribution, it is found that:
a) The pilot is at the 72th percentile.
b) 19.13% of pilots are unable to fly.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:

- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
.
Item a:
The percentile is the <u>p-value of Z when X = 74.2</u>, hence:


Z = 0.59
Z = 0.59 has a p-value of 0.7224.
72th percentile.
Item b:
The proportion that is able to fly is the <u>p-value of Z when X = 78 subtracted by the p-value of Z when X = 70</u>, hence:
X = 78:


Z = 2
Z = 2 has a p-value of 0.9772.
X = 70:


Z = -0.96
Z = -0.96 has a p-value of 0.1685.
0.9772 - 0.1685 = 0.8087 = 80.87%.
Hence the percentage that is unable to fly is:
100 - 80.87 = 19.13%.
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False, the upper quartile of a set of data is the median, not the mode