Midterm

Midterm

Don’t leave anything blank. I can always find a way to give you some credit if you’ve made an attempt. Be sure to post any questions you have after the answers open. Unlike the word problems in your book, my word problems are not real.

The work you turn in by 11:59 P.M. on July 21^st must be your own. Please don’t get advice or suggestions from your spouse, child, friend, or co-worker who just finished a similar class. I’m happy to provide that advice and those suggestions and then you can resubmit, if you choose, so there is no reason to cheat.

1. (one point) A researcher collected BMI (Body Mass Index) of 50 students in an Engineering school. He found the mean BMI was much smaller than the median BMI. The reason for this might be___

1. Several students had much smaller BMI scores than the other students
2. Several students had much larger BMI scores than the rest
3. The researcher made some measurement errors
4. All the students had smaller BMI scores, compared to national average

2. (one point) In the graph, there are two distributions: A and B.We can know from the graph:

1. Distribution A has a bigger standard deviation than distribution B
2. Distribution B has a bigger standard deviation than distribution A
3. Distribution A and distribution B have the same standard deviation
4. We cannot tell which has a larger standard deviation from the graph

3. (one point) What is the level of measure for each of the following:

1. Winners in pie eating contest                       Ordinal
2. Salaries of people in our classroom Ratio
3. Colors of Skittles             Nominal
4. Freezing temperatures on Celsius scale Interval

4. (one point) Determine type of sampling used:

1. Police stopped every sixth driver for sobriety test Systematic sampling

1. 1003 adults were called after their phone

numbers were randomly generated by computer        Simple random sample

1. Stat Dept at UMGC collected data by randomly

selecting 5 stat class and surveying every student      Cluster sampling

1. I collected hat sizes from my family             Convenience sample

5. (two points) A simple random sample of pages of my dictionary was collected.  These are the number of words defined on each page. Find the measures of central tendency: mean, median, and mode.

51     63     64     43     43     69     43   39     53     63

Mean: 56.8      Median: 63      Mode: 58

There are 1769 pages. Estimate the total number of words in the dictionary. Is the estimate likely to be an accurate estimate of the total number of words in the English language?

Estimated: 171,476

6. (two points) The bi-monthly salaries for the 12 workers at my local Chick Fil-A are as follows:

Calculate the measures of variability: range, variance, and standard deviation. Create a frequency distribution table that includes relative and cumulative relative frequency. Then create a graph of your choosing.

Range: (Max – Min) = 521

Variance: (n-nẋ)^2 / 11 = 22653.66

Standard Deviation: sqrt S^2 = 150.511

7. (two points) I had 15 students last term who earned the following grades:

98   85   89   73   72   85   85   92   85    97   92   93   95   86   87

What is the 5 numbers summary for these students? Create a box plot for the data.

Minimun = 73

Q1 = 85

Median = 89

Q3 = 96

Maximun = 98

8. (two points) I developed an achievement test and normalized it on people throughout the country over a year. My test has scores that are normally distributed with a mean of 100 and a standard deviation of 20.

1. Find the probability that a randomly selected adult has IQ < 115

1. Find the probability that a randomly selected adult has IQ > 70

1. Find P_30, which is the IQ score at the 30th percentile.

1. What percentage of adults have scores between 80 and 120?

9. (two points) Ten peas are generated from parents having the green/yellow pair of genes so there is a 75% probability that an individual pea will have a green pod. Find the probability that

among the 10 offspring peas, no more than 6 have green pods.

10. (two points) I always wanted to give away my vast wealth, so I am going to have a lottery next year. You have to pick the five winning numbers from 1-35. Each randomly selected number is different and order doesn’t matter. What is the probability of your winning?

11. (two points) In a study of families with children with disabilities, group of 5 US households were randomly selected. In the table below, the random variable x represents the number of households among 6 that had a child with a disability living there.

1. Is this a probability distribution?

Yes, because the probability that any chosen family could have a child with disabilities.

1. What is the mean?

µ = 2.58

1. What is the standard deviation?

δ  = 1.06

12. (two points) I am going to roll two fair dice.

1. List the sample space

1. What is the probability that I will roll a 3 on one of them when I roll both at the same time?

Getting  a 3 on any dice when rolling two {(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (1,3), (2,3), (4,3), (5,3) and (6,3)}. There are 11 changes on 36 probabilities

1. 11/36 = 0.305 = 30%

1. What is the probability that I will roll no more than a sum of 7 when I roll them both?

Getting at least a sum of 7 = {(1,6), (2,5), (3,4), (4,3), (5,2), and (6,1)} There are 6 changes on 36 probabilities

6/36 = 0.166 = 17%

1. Define mutually exclusive

Mutually exclusive is define when two event cannot happen at the same time.

1. Define independent

Independent events occurs when the probability of one of the events does not affect the outcome of the other events.