Transcript Slide 1 - Milan C-2

Statistics
Review Chapter 6
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Normal Distributions
Control Charts
Z-score vs raw score
Table is area under curve to the left
Given area,find z-score
For binomial to approximate normal, np>5
and nq>5
• Continuity correction
1
• The running times of feature movies have a
mound shaped distribution with mean =110
minutes and standard deviation of 30 minutes.
• Use the empirical rule to find an interval
centered about the mean in which about 68% of
the data will fall
• Estimate a range of values centered about the
mean in which about 95% of the data will fall
2
• The percentage growth rate of stocks of
companies that specialize in recreation
equipment and appliances has a mound
shaped distribution with mean estimated to
be 13.1% and standard deviation 6.0%.
• Estimate a range of values centered about
the mean in which 68% of the data will fall
• Estimate a range of values centered about
the mean in which 95% of the data will fall
3
• The highway patrol has a target of 28 traffic tickets per
week with standard deviation 5 tickets per week for a
stretch of mountain highway. The number of tickets issued
for 15 consecutive weeks is given below. T= number of
week, x = number of tickets
• T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
• x 22 20 15 16 25 30 30 34 30 32 36 40 33 35 30
• Make a control chart for the data above
• Determine whether the process is in statistical control. If
not, specify which out of control signals are present
4
• Last fiscal year, the average number of defective
televisions produced by a factory each day was 17.6,
with standard deviation of 5.2. For the first 10 days of
this fiscal year, the number of defective televisions
produced is shown in the following table:
• Day 1 2 3 4 5 6 7 8 9 10
• Def tv 19 15 13 16 24 29 34 25 20 10
• Make a control chart for the daily number of defective
televisions produced
• Do the data indicate that the production is “in control;”?
Explain
5
• Troy took a standardized test to try to get credit
for first-year Spanish by examination. His
standardized score was 1.9. The mean score
for the exam was 100 with standard deviation
12. The language department requires a raw
score if 120 to get credit by exam for first-year
Spanish.
• Compute Troy’s raw score
• Will Troy get credit for first year Spanish based
on this exam?
6
• The snow pack on the summit of Wolf Creek
Pass, Colorado on March 1 has been measured
for many years. It is normally distributed with
mean 78.1 inches and standard deviation of
10.4 inches. A year is selected at random.
• Find the probability that the snowpack is less
than 60 inches
• Find the probability that the snowpack is more
than 85 inches
• Find the probability that the snowpack is
between 60 and 85 inches
7
• The life of Corn Delight popcorn maker is
normally distributed with mean 20 months and
standard deviation 2 months. The manufacturer
will replace a Corn Delight popper is it breaks
during the guarantee period.
• If the manufacturer guarantees the popper for 18
months what fraction of the poppers will he
probably have to replace
• How long should the guarantee period be if the
manufacturer does not want to replace more
than 3% of the poppers
8
• Let x represent the life the a AA battery in
a portable radio. The x distribution has
mean 44 hours and standard deviation 3.6
hours. Convert each of the following x
intervals into z intervals.
• 40 < x < 46
• 37 < x < 51
• 41 < x < 45
9
• David and Laura are both applying for a position of the ski patrol.
David took the advanced first aid class at his college. His score on
the comprehensive final exam was 173 points. The final exam
scores followed a normal distribution with mean 150 points and
standard deviation 25 points. Laura took an advanced first aid class
at the plant where she works, For the method of testing there her
cumulative scored on all exams was 88. The cumulative scores
followed a normal distribution with mean 65 and standard deviation
10. Both courses are comparable in content and level of difficulty.
There is only one position available on the ski patrol and David and
Laura are equally qualified skiers.
• Both David and Laura scored 23 points above the mean for their
respective tests. Does this mean they both gave the same
performance on the first aid course? Explain
• Calculate the z scores for David and Laura. On the basis of test
results which of them should get the job. Explain
10
• A certain portable CD player is known to
function properly for a mean 3.6 years with
a standard deviation of .6 year. The
player is sold with a 3 year warranty.
What is the probability that the player will
break during the warranty period?
11
• Find z such that 80% of the area under the
standard normal curve lies between –z
and z
12
• The probability of an adverse reaction to a flu
shot is 0.02. It the shot is given to 1000 people
selected at random, what is the probability that:
• 15 or fewer people will have an adverse reaction
• 25 or more people will have an adverse reaction
• Between 20 and 30 people will have an adverse
reaction
13
• On Professor Grindstone’s final exam, the mean
score was 78 and the standard deviation was
10. He wants to “curve” the exam so that the
middle 50% of the students get C’s.
• Find a z score for which the area under the
standard normal curve form –z to z is 50%
• Find the range of schores which will be assigned
a grade of C
14
• The number of visitors per day at a
national park during the summer months
follows a normal distribution with mean
10500 and standard deviation 2750. For a
summer day chosen at random,
• Find the probability that the number of
visitors will be between 6000 and 15000
• Find the probability that the number of
visitors will be less than 5000