 # “1. For a standard normal distribution, find: P(z &lt; -...

## Question

“1. For a standard normal distribution, find:

2. For a standard normal distribution, find:

3. For a standard normal distribution, find:
P(0.03 < z < 2.69) Round your answer to three decimal places.

4. For a standard normal distribution, given:
P(z < c) = 0.2801

5. For a standard normal distribution, find:
P(z > c) = 0.0153
Find C.

6. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10 years, and standard deviation of 3.2 years.
If you randomly purchase one item, what is the probability it will last longer than 6 years? Round your answer to three decimal places.

7. A particular fruit's weights are normally distributed, with a mean of 648 grams and a standard deviation of 7 grams.
If you pick one fruit at random, what is the probability that it will weigh between 643 grams and 661 grams? Round your answer to three decimal places.

8. About % of the area under the curve of the standard normal distribution is between z=−0.125 and z=0.125 (or within 0.125 standard deviations of the mean). Round your answer to two decimal places.

9. The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 30 liters, and standard deviation of 6 liters.

A) What is the probability that daily production is less than 18.5 liters?

B) What is the probability that daily production is more than 27.8 liters?

Warning: Do not use the Z Normal Tables...they may not be accurate enough since WAMAP may look for more accuracy than comes from the table.

10. The combined SAT scores for the students at a local high school are normally distributed with a mean of 1469 and a standard deviation of 293. The local college includes a minimum score of 590 in its admission requirements.

What percentage of students from this school earn scores that fail to satisfy the admission requirement?
P(X < 590) = %

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

11. A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1117 and a standard deviation of 196. Scores on the ACT test are normally distributed with a mean of 20.5 and a standard deviation of 4. It is assumed that the two tests measure the same aptitude, but use different scales.

If a student gets an SAT score that is the 58-percentile, find the actual SAT score.
SAT score =
Round answer to a whole number.

What would be the equivalent ACT score for this student?
ACT score =
Round answer to 1 decimal place.

If a student gets an SAT score of 1372, find the equivalent ACT score.
ACT score =
Round answer to 1 decimal place.

12. Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher’s hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a Normal model with mean μ = 92.12 mph and a standard deviation of σ = 2.43 mph.

Compute the z-score of pitch with speed 94.1 mph. (Round your answer to two decimal places.)

Approximately what fraction of these four-seam fastballs would you expect to have speeds between 92.6 mph and 93.4 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.)

Approximately what fraction of these four-seam fastballs would you expect to have speeds above 93.4 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.)

A baseball fan wishes to identify the four-seam fastballs among the slowest 10% of all such pitches. Below what speed must a four-seam fastball be in order to be included in the slowest 10%? (Round your answer to the nearest 0.1 mph.)

13.A population of values has a normal distribution with μ=71.7 and σ=31.1. You intend to draw a random sample of size n=10.

Find the probability that a single randomly selected value is less than 54.
P(X < 54) =

Find the probability that a sample of size n=10 is randomly selected with a mean less than 54.
P(M < 54) =

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

14. Scores for a common standardized college aptitude test are normally distributed with a mean of 503 and a standard deviation of 113. Randomly selected men are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect.

If 1 of the men is randomly selected, find the probability that his score is at least 560.2.
P(X > 560.2) =

If 10 of the men are randomly selected, find the probability that their mean score is at least 560.2.
P(M > 560.2) =

Assume that any probability less than 5% is sufficient evidence to conclude that the preparation course does help men do better. If the random sample of 10 men does result in a mean score of 560.2, is there strong evidence to support the claim that the course is actually effective?

No. The probability indicates that it is too possible by chance alone to randomly select a group of students with a mean as high as 560.2.
Yes. The probability indicates that it is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 560.2.

15. The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 39 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 39 and 53?

Do not enter the percent symbol.

16. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 56 months and a standard deviation of 6 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 44 and 50 months?

Do not enter the percent symbol.

## Solution Preview

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1. For a standard normal distribution, find:

Solution:
We need to find
P(Z < -0.21)
=0.5- P(0< Z < 0.21)
= 0.5 - 0.0832
= 0.4168
Answer for 3 decimal places is 0.417
2. For a standard normal distribution, find:

Solution:
We need to find
P(Z > 1.56)
=0.5- P(0< Z < 1.56)
= 0.5 - 0.4406
= 0.0594
Answer for 3 decimal places is 0.059...

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