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COACHING ACTUARIES MATH STAT VEE QUESTIONS AND VERIFIED ANSWERS|100 CORRECT|GRADE A+
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COACHING ACTUARIES MATH STATVEE QUESTIONS AND VERIFIED
ANSWERS|100 CORRECT|GRADE A+
An agency has ten left-handers and twenty right-handers. Five individuals are chosen for a survey using
simple random sampling.
Calculate the probability all five have the same handedness. - ANSWER 0.11
There are 97 men and 3 women in an organization. A simple random sample of 5 people is taken to form
a committee.
What is the probability that the committee includes all 3 women? - ANSWER 6.2×10−5
A marine scientist has six ocean water samples that are evenly split between the Pacific and Atlantic
oceans. Four of the ocean water samples are chosen using simple random sampling.
Find the probability that all the Pacific ocean samples are chosen. - ANSWER 1/5
A random sample X1�1, X2�2, ..., X10�10 is drawn from a normal distribution with variance 12. Let X¯�¯
be the sample mean.
Let χ2p,ν��,�2 be the 100p�th percentile of a chi-squared random variable with ν� degrees of freedom.
The following table lists values of χ2p,ν��,�2 for specific combinations of p� and ν�:
Find the probability that ∑10i=1(Xi−X¯)2∑�=110(��−�¯)2 is greater than 120. - ANSWER At least 0.3, but
less than 0.4
A manufacturer makes golf balls with a mean weight of 1.62 ounces and a standard deviation of 0.05
ounces. A random sample of 100 balls are taken.
Using the Central Limit Theorem, approximate the probability that the sample mean weight of the 100
balls is between 1.615 and 1.625 ounces. - ANSWER 0.68
IPO returns from the real estate sector are normally distributed with mean μ�. An analyst takes a
random sample of 12 IPOs from the real estate sector.
Let X¯�¯ and S2�2 be the sample mean and sample variance of the 12 IPO returns, respectively.
,Let tp,ν��,� be the 100p�th percentile of a t� random variable with ν� degrees of freedom. The
following table lists values of tp,ν��,� for specific combinations of p� and ν�:
What is the probability that X¯−μS�¯−�� is less than 0.51? - ANSWER 0.95
You are given the following information from a random sample:
Xi�� is normally distributed with mean 1 and variance 2.
Sample size is 20.
S2�2 is the unbiased sample variance.
Let χ2p,ν��,�2 be the 100p�th percentile of a chi-squared random variable with ν� degrees of freedom.
The following table lists values of χ2p,ν��,�2 for specific combinations of p� and ν�:
Calculate c�, such that Pr(S2≤c)=0.95Pr(�2≤�)=0.95. - ANSWER At least 3.1
A random sample X1�1, X2�2, ..., Xn�� is drawn from a normal distribution with mean μ�.
You are given:
X¯�¯ is the sample mean.
S� is the unbiased sample standard deviation.
V=X¯−μS/n−−√�=�¯−��/�
The 20th percentile of V� is −0.8583−0.8583.
Calculate Pr(|V|<0.8583)Pr(|�|<0.8583). - ANSWER 0.6
A class has 8 boys and 7 girls. Using simple random sampling, the teacher selects 3 of the children for a
special project.
Calculate the probability that two girls and one boy are selected. - ANSWER 0.369
Out of 50 basketball players trying to make a team, 5 will be chosen. 36 of the 50 are seniors and the
remaining players are juniors. The manager wants 2 seniors and 3 juniors to make the team.
What is the probability of meeting the manager's objectives if players were selected by simple random
sampling? - ANSWER 0.108
, You are given the following information about a random sample of claim amounts:
Claim severity follows a Pareto distribution with α=3�=3 and θ=50�=50, with mean and variance given by
mean=θα−1,variance=2θ2(α−2)(α−1)−(θα−1)2mean=��−1,variance=2�2(�−2)(�−1)−(��−1)2
The sample size is 100.
Using the Central Limit Theorem, calculate the probability that the sample mean claim amount will lie
between 30 and 35. - ANSWER At least 8%
Claims filed under a group of auto insurance policies have normally distributed amounts with mean
19,400 and standard deviation 5,000. A random sample of 25 claims are taken.
What is the probability that the average of the 25 claim amounts exceeds 20,000? - ANSWER 0.27
An auto insurer has a random sample of 800 claims. The claim amounts have a mean of 2,000 and a
variance of 136,875.
Using the Central Limit Theorem, approximate the 99th percentile of the total claim amount from the
sample. - ANSWER 1,624,000
Net profits from movies filmed by Merdeka Studios follow a normal distribution with mean 2.7. A
random sample of six movies are examined.
Let tp,ν��,� be the 100p�th percentile of a t� random variable with ν� degrees of freedom. The
following table lists values of tp,ν��,� for specific combinations of p� and ν�:
Find the probability that the sample mean net profit is greater than 2.7 minus three-fourths of the
sample standard deviation. - ANSWER At least 0.93, but less than 0.94
Let X1�1, X2�2, ..., Xn�� denote a random sample from a normal distribution with variance σ2�2.
You are given:
X¯�¯ is the sample mean.
W=∑ni=1(Xi−X¯)2σ2�=∑�=1�(��−�¯)2�2
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