**Math 1635**

**Exam I**

**Fall 2020**

Instructions were emailed to you, and discussed in Tuesday’s lecture.

1. (10 pts) Please report the grade point average, rounded to 3 digits. Do not round the middle steps.

**Course**

**Credits**

**Grade**

Religion

3

A

Relativity

4

C

Renaissance Art

3

B

Russian Folk Songs

1

B

2. (10 pts) Let X represent the number of pets are in a household, and p(X) is the proportion (or probability) of households with X pets. Please report EX as an integer divided by a power of 10 (the smallest power of 10 for which the numerator is an integer). Note that p(X=3) has purposely been left blank, but do not assume it equals zero.

X

0

1

3

5

P(X)

0.10

0.40

0.30

3. (10 pts) Is the max an upper outlier for the distribution with the following 5 Number Summary? Justify with calculations. The 5 Number Summary is {90, 50, 45, 40, 25}.

4. (10 pts) In a certain course your semester grade is determined by marks on 4 exams, each worth 100 points. Your marks on the first 3 exams were 82, 89 and 94. What mark would you need on the 4th exam for an A in the course? (For an A your average must be at least 90.0).

5. (15 pts) A bell-shaped curve has µ = 52, σ = 2. Please report an interval around µ that contains exactly 95% of the data. Use correct interval notation.

6. (10 pts) If you are in a class with 95 students (you are one of the 95) and 11 others have test marks that exceed yours, what is your percentile?

7. (15 pts) Suppose the distribution of hours of sleep among undergraduates is normal with µ = 8 hrs, σ = 2 hrs. Let X represent the amount of sleep by a randomly chosen undergraduate. Please report these probabilities:

a. P(X> 6hrs) b. P(X < 10hrs)

8. (15 pts) How much time do people spend in traffic? A random sample of n = 81 has reported ????, s = 2 min. Please report a 95% confidence interval for µ. As part of your answer please interpret the number 95%.

9. (5 pts)

If sample size is increased but confidence level is kept constant, what would be the effect on confidence intervals?

If sample size is kept constant but confidence level is increased, what would be the effect on confidence intervals?

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