A box contains 2000 red beans and 3000 green beans. Pick up 10 beans at random without replacement. What is the probability of getting at most 2 red beans?  If applicable, you can use some approximation method to get the probability. 

Adult females have forearm lengths (in inches) that are normally distributed with mean 17.75. and variance 0.36. Find the upper quartile length of a female’s forearm – that is, a length x that is exceeded by 25% of adult females.

A random variable X has a density function . Find the variance of X.

Two discrete random variables X and Y have a joint probability function f(x,y) given in the following table: f(x,y) x=0 1 2 y=0 0.30 0.12 0.18 1 0.20 0.12 0.08 Find the mean of Y.

A prescription drug firm wants to know the effectiveness of a new drug in animal test, that is, percentage (p) of diseased animals cured after the use of the drug. So, the form has to run some tests.  The firm uses the sample proportion to estimate p and wishes that the maximum error is less than 3% with 95% confidence. Find the minimal number of tests that are required to run.  

A prescription drug firm wants to know the effectiveness of a new drug in animal test, that is, percentage (p) of diseased animals cured after the use of the drug. So the form has to run some tests.  Suppose that the firm arranges 50 tests and it turns out that 24 animals are cured after the use of the drug. Give a point estimate for p.  

The following observations are the numbers of calls received by an office in ten working days.                4 , 4,  2,  3,  8,  9,  3,  4,  3,  4 Find the mode(s).  

A random sample of size 10 is as follows:             2.3,  4.3, 12.6,  4.2,  1.0,  4.5,  4.1,  8.5,  4.0,  4.8                               Find the sample mean.

The following observations are the numbers of calls received by an office in ten working days.                4 , 4,  2,  3,  8,  9,  3,  5,  3,  4 Find the third quartile.

A random sample of size 10 is as follows:         0.5,  1.8,   0.2,    0.5,   0.0,   1.0,   1.3,   2.3,   0.2,   0.8 Find all the mode(s).