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Questions on Probabilities and Statistical Distributions

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1. Heights of men on a baseball team have a bell-shaped distribution with a mean of 185cm and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?
a. 167cm and 203cm
b. 179cm and 191cm

2. Heights of women have a bell-shaped distribution with a mean of 159cm and a standard deviation of 8cm. Using Chebyshevs theorem, what do we know about the percentage of women with heights that are within 3 standard deviations of the mean? What are the minimum and maxium heights that are within 3 standard deviations of the mean?
At least ____% of women have heights with 3 standard deviaitons of 159cm.
Miminum height____cm
Maxium height______cm

3. Determime whether the distribution is a discrete probability distribution. Why or why not?
x P(x)
0 0.28
1 0.32
2 -0.20
3 0.32
4 0.28

4. Assume that a procedure yields a binomial distrubution with a trail repeated n times. Use a binomial probabilities table to find the probability of x successes given the probability p of success on a given trail
n=2, x=1, p=0.40
P(1)=_______ (round to 3 decimal places if needed)

5. In a region 90% of the population have brown eyes. If 12 people are randomly selected, find the probability that at least 10 of them have brown eyes. Is it unusual to randomly select 12 people and find that at least 10 of them have brown eyes? Why or why not?
The probability that at least 10 of 12 people selected have brown eyes______(round 3 places if needed)
Is it unusual to randomly select 12 people and find that at least 10 of them have brown eyes. Note that a small probability is one that is less than 0.05.______

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The solution gived detailed steps on solving various questions on probabilities and statistical distributions. All formula and calculations are shown and explained.

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1.
a. 167cm and 203cm
203-185=185-167=18=3 standard deviation, by empirical rule, percentage = 99.7%

b. 179cm and 191cm
191-185=185-179=6=1 standard ...

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