1.A particular fruit's weights are normally distributed, with a mean of 313 grams and a standard deviation of 21 grams.
The heaviest 4% of fruits weigh more than how many grams?
Give your answer to the nearest gram.
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2.The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 40 liters, and standard deviation of 11.1 liters.
A) What is the probability that daily production is less than 31.7 liters?
Answer= (Round your answer to 4 decimal places.)
B) What is the probability that daily production is more than 46.5 liters?
Answer= (Round your answer to 4 decimal places.)
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.
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3.A distribution of values is normal with a mean of 87.7 and a standard deviation of 59.8.
Find P6, which is the score separating the bottom 6% from the top 94%.
P6 =
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
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4.The combined SAT scores for the students at a local high school are normally distributed with a mean of 1513 and a standard deviation of 295. The local college includes a minimum score of 1867 in its admission requirements.
What percentage of students from this school earn scores that fail to satisfy the admission requirement?
P( X < 1867) = %
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.
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5. 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 87.2 mph. (Round your answer to two decimal places.)
Approximately what fraction of these four-seam fastballs would you expect to have speeds between 92.3 mph and 96.3 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 below 92.3 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 fastest 18% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 18%? (Round your answer to the nearest 0.1 mph.)
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6.Scores for a common standardized college aptitude test are normally distributed with a mean of 512 and a standard deviation of 98. 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 561.5.
P( X > 561.5) =
Enter your answer as a number accurate to 4 decimal places.
If 19 of the men are randomly selected, find the probability that their mean score is at least 561.5.
P( M > 561.5) =
Enter your answer as a number accurate to 4 decimal places.
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 19 men does result in a mean score of 561.5, is there strong evidence to support the claim that the course is actually effective?
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7.A population of values has a normal distribution with μ=44.5 and σ=14.5 . You intend to draw a random sample of size n=189.
Find the probability that a single randomly selected value is less than 44.3.
P(X < 44.3) =
Find the probability that a sample of size n=189 is randomly selected with a mean less than 44.3.
P(M < 44.3) =
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.
A population of values has a normal distribution with μ=145.4 and σ=32.4. You intend to draw a random sample of size n=196.
Find P2, which is the score separating the bottom 2% scores from the top 98% scores.
P2 (for single values) =
Find P2, which is the mean separating the bottom 2% means from the top 98% means.
P2 (for sample means) =
Enter your answers as numbers accurate to 1 decimal place.
************NOTE************ round your answer to ONE digit after the decimal point! ***********
Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
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8.The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 50 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 36 and 50?
Do not enter the percent symbol.
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9.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 46 months and a standard deviation of 8 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 22 and 38 months?
Do not enter the percent symbol.
