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Solving problems, not by copying answeIS.
Question 1
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A normal distribution has a mean of 122 and a standard deviation of 3. Find the z-
score for a data value of 128.
2
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Question 2
Round to two decimal places
2/2 pts 1 2 Details
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GPAs at CCSU are normally distributed with a mean of 2.31 and a standard deviation
of 0.48. Find the z-score for a GPA of 2.89.
○ 0.4792
01.021
○ 0.2500
0 1.479
1.208
○ 0.2292
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Question 3
2/2 pts 12 Details
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Adult men have an average height of 69.0 inches with a standard deviation of 2.8
inches. Find the height of a man with a z-score of -0.21. Round your answer to one
decimal place.
68.4
o inches
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Question 4
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A manufacturer knows that their items have a normally distributed lifespan, with a
mean of 6.7 years, and standard deviation of 1.1 years.
If you randomly purchase one item, what is the probability it will last longer than 8
years?
Round answer to three decimal places
0.119
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Question 5
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Assume that the readings at freezing on a batch of thermometers are normally
distributed with a mean of 0°C and a standard deviation of 1.00°C. A single
thermometer is randomly selected and tested. Find P67, the 67-percentile. This is the
temperature reading separating the bottom 67% from the top 33%.
P67
= 0.440
°C
(Round answer to three decimal places)
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Question 6
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A manufacturer knows that their items have a normally distributed length, with a
mean of 12.2 inches, and standard deviation of 1.2 inches.
If one item is chosen at random, what is the probability that it is less than 13.2 inches
long?
0.7967
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2/2 pts 12 Details
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The scores on the Accuplacer test and High School GPAs are normally distributed.
The Accuplacer test had a mean of 30 and a standard deviation of 8.
High School GPAs had a mean of 2.9 and a standard deviation of 0.2.
What high school GPA do you need to equal a score of 56 on the Accuplacer test?
Give answer to two decimal places.
3.55
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Question 12
2/2 pts 1 2 Details
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A manufacturer knows that their items have a normally distributed lifespan, with a
mean of 8.5 years, and standard deviation of 2.6 years.
The 2% of items with the shortest lifespan will last less than how many years?
Give your answer to one decimal place.
3.2
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Question 16
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A distribution of values is normal with a mean of 169.9 and a standard deviation of
26.4.
Find the probability that a randomly selected value is less than 222.7.
<
P(X 222.7)
0.9772
Enter your answer as a number accurate to 4 decimal places. Answers obtained using
exact z-scores or z-scores rounded to 3 decimal places are accepted.
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Question 17
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Let X represent the full height of certain species of tree. Assume that X is normally
distributed with a mean of 26.9 feet and a standard deviation of 98.4 feet.
Find the probability that the full height of a randomly selected tree is greater than
194.2 feet.
P(X > 194.2) = 0.0446
Enter your answer as a number accurate to 4 decimal places.
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