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Adult females have forearm lengths that are normally distributed with mean 17.75 in. and standard deviation 0.65 in. Find the upper quartile length of a female’s forearm – that is, a length x that is exceeded by 25% of adult females.

Suppose 64 observations are sampled from a normal population with mean 5 and standard deviation 4. Let  

Suppose we have 20 observations from a normal population with mean  10 and variance 3. Let  

Suppose we have 20 observations from a normal population with mean 10 and standard deviation 3. Let  

Suppose we have 20 observations from a normal population with mean  10 and standard deviation 3. Let  

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).

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

The life, in years, of a certain type of light bulbs has an exponential distribution with an average life β = 1. A statistician decides to test these bulbs for their lifetimes one after another until he finds the second light bulb whose lifetime is more than 5 years.  Use X to denote the light bulbs he will use for his test. What is the distribution function of X?    (Name of the distribution)

The life, in years, of a certain type of electrical switch has an exponential distribution with an average life β = 0.5.  Randomly select one switch and install it in a system, what is the probability the switch fails during the first year?

For a normal variable X with mean 10 and standard deviation 5, find the value of k such that P(X