PROBLEM 1 According to statistics from the U.S. National Eye Institute, that 8% of Caucasian men and 0.5% of Caucasian women have some form of color vision deficiency (aka “color blindness”). Assume that women and men exist in equal number

PROBLEM 1

According to statistics from the U.S. National Eye Institute, that 8% of Caucasian men and 0.5% of Caucasian women have some form of color vision deficiency (aka “color blindness”). Assume that women and men exist in equal number in the U.S. population.

1. [5pt] What is the probability that a random person, X, from this population is color blind?
2. [5pt] An eye doctor is seeing a Caucasian patient who is known to be color blind. Calculate the probability that this patient is male.

PROBLEM 2  

Terpz4LYF produces clocks that count down the time until a Terp graduates from UMD. They market these clocks to alumni, who purchase the clock when a future Terp is born. Your parents purchased this clock for you! But is it reliable? Let’s find out.

The clock has a time to failure distribution given by the following:

Find:

1. [5pt] The reliability of the clock at 21 years.
2. [5pt] The MTTF of the clock.
3. [5pt] The hazard rate function.
4. [5pt] Do you consider this a reliable product? Explain why.

PROBLEM 3

You are given the following grouped data. Your supplier has told you that the failure times for this widget are normally distributed. You want to conduct a test to be sure. Use

1. [10pts] Use the data to estimate the parameters of the normal distribution
2. [10pts] Use a chi-squared test to test the hypothesis that these data come from a normal distribution with the parameters you estimated. Discuss the interpretation of the test.

Critical Values of Chi-Square  Distribution Function