6.7 Homework

Consider the following experiment. You are one of 100 people enlisted to take part in a study to determine the percent of nurses in America with an R.N. (registered nurse) degree. You ask nurses if they have an R.N. degree. The nurses answer “yes” or “no.” You then calculate the percentage of nurses with an R.N. degree. You give that percentage to your supervisor.

• a What part of the experiment will yield discrete data?
• b What part of the experiment will yield continuous data?

When age is rounded to the nearest year, do the data stay continuous, or do they become discrete? Why?

Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform Distribution from 1 – 53 (spread of 52 weeks).

• a $X~$
• b Graph the probability distribution.
• c $f(x)=$
• d $\mu =$
• e $\sigma =$
• f Find the probability that a person is born at the exact moment week 19 starts. That is, find $P(x=\text{19})=$
• g
• h Find the probability that a person is born after week 40.
• i $$
• j Find the 70th percentile.
• k Find the minimum for the upper quarter.

A random number generator picks a number from 1 to 9 in a uniform manner.

• a $X\text{~}$
• b Graph the probability distribution.
• c $f(x)=$
• d $\mu =$
• e $\sigma =$
• f
• g $P(x>5\text{.}\text{67})=$
• h $P(x>5\mid x>3)=$
• i Find the 90th percentile.

The time (in minutes) until the next bus departs a major bus depot follows a distribution with $f(x)=\frac{1}{\text{20}}$ where $x$ goes from 25 to 45 minutes.

• a Define the random variable. $X=$
• b $X\text{~}$
• c Graph the probability distribution.
• d The distribution is ______________ (name of distribution). It is _____________ (discrete or continuous).
• e $\mu =$
• f $\sigma =$
• g Find the probability that the time is at most 30 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
• h Find the probability that the time is between 30 and 40 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
• i _________. State this in a probability statement (similar to g and h ), draw the picture, and find the probability.
• j Find the 90th percentile. This means that 90% of the time, the time is less than _____ minutes.
• k Find the 75th percentile. In a complete sentence, state what this means. (See j .)
• l Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 minutes.

According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between 6 and 15 pounds a month until they approach trim body weight. Let’s suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month. (Source: The McDougall Program for Maximum Weight Loss by John A. McDougall, M.D.)

• a Define the random variable. $X=$
• b $X\text{~}$
• c Graph the probability distribution.
• d $f(x)=$
• e $\mu =$
• f $\sigma =$
• g Find the probability that the individual lost more than 10 pounds in a month.
• h Suppose it is known that the individual lost more than 10 pounds in a month. Find the probability that he lost less than 12 pounds in the month.
• i __________. State this in a probability question (similar to g and h), draw the picture, and find the probability.