Prob and Stats 3.4

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Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years. Given the quartiles Q1=1.840​, Q2=3.150​, and Q3=4.830​, compute the interquartile​ range, IQR.

IQR= 2.99

A manufacturer of bolts has a​ quality-control policy that requires it to destroy any bolts that are more than 4 standard deviations from the mean. The​ quality-control engineer knows that the bolts coming off the assembly line have mean length of 14 cm with a standard deviation of 0.05 cm. For what lengths will a bolt be​ destroyed?

A bolt will be destroyed if the length is less than 6.9 cm or greater than 7.1 cm.

Explain the meaning of the following percentiles in parts​ (a) and​ (b). ​(a) The 5th percentile of the weight of males 36 months of age in a certain city is 13.0 kg. ​(b) The 90th percentile of the length of newborn females in a certain city is 53.8 cm.

(a) 5​% of​ 36-month-old males weigh 13.0 kg or​ less, and 95​% of​ 36-month-old males weigh more than 13.0 kg. (b) 90​% of newborn females have a length of 53.8 cm or​less, and 10​% of newborn females have a length that is more than 53.8 cm.

The following graph is an ogive of a standardized​ test's scores. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile. Complete parts a through c.

(a) Find and interpret the percentile rank of a test score with a value of 130 A test score of 130 corresponds to the 50th percentile rank since this percentage of test scores are less than or equal to a test score with a value of 130. (b) A test score of 150 corresponds to the 90th percentile rank since this percentage of test scores are less than or equal to a test score with a value of 150. (c) What score corresponds to the 10th percentile? The 10th percentile corresponds to a test score of 110

Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years. Determine the quartiles.

Q1= 1.91 Q2= 9.01 Q3= 4.505

​_______ divide data sets in fourths.

Quartiles

A highly selective boarding school will only admit students who place at least 2.5 standard deviations above the mean on a standardized test that has a mean of 100 and a standard deviation of 20. What is the minimum score that an applicant must make on the test to be​ accepted? 2.5=x-100/20 2.5x20=x-100 50=x-100 x=150

The minimum score that an applicant must make on the test to be accepted is 150

In a certain​ city, the average​ 20- to​ 29-year old man is 69.8 inches​ tall, with a standard deviation of 3.2 ​inches, while the average​ 20- to​ 29-year old woman is 64.3 inches​ tall, with a standard deviation of 3.8 inches. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman?

The z-score for the man, 1.63, is larger than the z-score for the women, 1.5, so he is relatively taller.

The​ _______ represents the number of standard deviations an observation is from the mean.

z-score

The accompanying data represent the wait time​ (in minutes) for a random sample of forty visitors to an amusement park ride. Complete parts​ (a) and​ (b). 6 14 4 6 5 32 6 6 24 9 8 44 10 11 31 0 27 4 8 6 20 7 21 9 26 16 54 3 10 30 0 4 5 10 5 7 8 16 9 14 (b) Does the data set have​ outliers? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

​(a) By the​ quartiles, about 25% of the wait times are Q1=6 minute (s) or less, and about 75% of the wait times exceed Q1 minute (s), about 50% of the wait times are Q2=9 minutes or less and about 50% of the wait time exceed Q2 minutes; about 75% of the wait times are Q2=17 minutes or less, and about 25% of the wait times exceed Q3 minutes. (b)

Violent crimes include​ rape, robbery,​ assault, and homicide. The following is a summary of the​ violent-crime rate​ (violent crimes per​ 100,000 population) for all states of a country in a certain year. Q1=272.8​, Q2=387.9​, Q3=529.7

​25% of the states have a​ violent-crime rate that is 272.8 crimes per​ 100,000 population or less.​ 50% of the states have a​ violent-crime rate that is 387.9 crimes per​ 100,000 population or less.​ 75% of the states have a​ violent-crime rate that is 529.7 crimes per​ 100,000 population or less.


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