Prob and Stats 3.4
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 orless, 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.
