# STAT-2903 Study Guide - Final Guide: Poisson Distribution, Richter Magnitude Scale, Blood Pressures

by OC16583

School

University of WinnipegDepartment

STATISTICSCourse Code

STAT-2903Professor

Bob BectorStudy Guide

FinalThis

**preview**shows page 1. to view the full**5 pages of the document.**STAT-1201 Introduction to Statistical Analysis, SAMPLE Final Exam

Special Instructions:

1. FORMULAE ARE SECTION SPECIFIC.

YOUR INSTRUCTOR WILL PROVIDE YOU WITH THE FORMULAE SHEET.

2. Necessary statistical tables are provided.

3. Show all your work in the examination booklet provided.

4. Only non-programmed hand calculators may be used.

5. Whenever necessary state H0and H1clearly and draw appropriate conclusions.

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PART A: 70 MARKS

– Answer any 10 of the following 12 questions.

– Each is worth 7 marks

1. The change in temperature between the warmest and coolest parts of the day measures

the sun’s thermal heating of the earth (called Diurnal Temperature Variation).

Temperature changes (in ◦F) for ten days are recorded as follows:

11.3 10.3 11.6 14.5 15.2 13.9 13.6 11.0 16.0 16.0

(a) Determine the median, and also the ﬁrst and third quartiles.

(b) Determine the sample mean and the sample standard deviation.

(c) Determine the percentage of observations that falls within 2 standard

deviations of the mean.

2. The probability that one drug-resistant bacterium will be killed by the application of a

ﬁrst-line drug Ais 0.6, and the probability that the bacterium will be killed by a more

costly second-line drug Bis 0.7; the probability that both drugs will kill the bacterium

(A∩B) is 0.50.

(a) What is the probability that the bacterium is killed by at least one of the

drugs applied?

(b) What is the probability that the bacterium is not killed by either of the two

drugs applied?

(c) Are events Aand Bmutually exclusive? Explain.

(d) Are events Aand Bindependent? Explain.

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3. (a) A hockey goalie has a 0.89 chance per shot of preventing a goal. What is the

probability that, out of ten shots taken, exactly one goal occurs.

(b) For a recent period of 100 years, the average number per year of major

earthquakes (at least 6.0 on the Richter scale) was 0.93. Assuming that the

Poisson distribution is a suitable model, ﬁnd the probability that no

earthquakes occur in a year.

(c) In an experiment for cross-breeding, there are eight tropical ﬁsh of which ﬁve

are female. If four ﬁsh are selected at random without replacement, ﬁnd the

probability that exactly two are female.

4. The average of sodium content in a certain brand of low-salt microwave frozen dinners is

660 mg, and the standard deviation is 35 mg. Assume the variable is normally

distributed.

(a) If a single dinner is selected, ﬁnd the probability that the sodium content will

be more than 670 mg.

(b) If a sample of 10 dinners is selected, ﬁnd the probability that the mean of the

sample will be larger than 670 mg.

(c) Why is the probability for part (a) greater than that for part (b)?

5. Given that the heights of all female college basketball players have a normal distribution

with a mean of 68 inches and a standard deviation of 2 inches, you extract a random

sample of 16 female college basketball players.

(a) Find the probability that the mean height of the sample will be more than

68.8 inches.

(b) Determine the 97th percentile of the distribution of the sample mean.

6. (a) A survey of 1275 Canadians indicated that 1224 prefer buying products that

can be recycled. Find a 95% conﬁdence interval for the true population

proportion.

(b) A survey of 1100 hospital admissions reports that the average length of stay

for seniors aged 65 and over who are hospitalized for falls is 13 days. Find a

point estimate of the population mean. Find the 98% conﬁdence interval of

the true mean. Assume the population standard deviation was 1.3 days.

7. (a) The standard deviation of the viscosity of a brand of engine oil is 0.02. How

large a sample would be needed for a 95% conﬁdence interval to be within

0.005 units of the population mean?

(b) A maker of diet meals claims that the average calorie content of its meals is

800. A researcher tested 12 meals and found that the average number of

calories was 873 with a standard deviation of 25. Does the evidence support

the claim at α= 0.05? Assume normality of the population.

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