A certain brand of automobile tire has a mean life span of 34,000 miles and a standard deviation of 2,050 miles.​ (Assume the life spans of the tires have a​ bell-shaped distribution.)       Question content area bottom Part 1 ​(a) The life spans of three randomly selected tires are 33,000 ​miles, 36,000 ​miles, and 31,000 miles. Find the​ z-score that corresponds to each life span.   For the life span of 33,000 ​miles, z-score is negative 0.49   −0.49. ​(Round to the nearest hundredth as​ needed.) Part 2 For the life span of 36,000 ​miles, z-score is 0.98   0.98. ​(Round to the nearest hundredth as​ needed.) Part 3 For the life span of 31,000 ​miles, z-score is negative 1.46   −1.46. ​(Round to the nearest hundredth as​ needed.) Part 4 According to the​ z-scores, would the life spans of any of these tires be considered​ unusual?     Yes   No Your answer is correct. Part 5 ​(b) The life spans of three randomly selected tires are 29,900 ​miles, 38,100 ​miles, and 34,000 miles. Using the empirical​ rule, find the percentile that corresponds to each life span.   The life span 29,900 miles corresponds to a percentile of enter your response here   . The life span 38,100 miles corresponds to a percentile of enter your response here   . The life span 34,000 miles corresponds to a percentile of enter your response here   . ​(Round to the nearest whole number as​ needed.)

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A certain brand of automobile tire has a mean life span of
34,000
miles and a standard deviation of
2,050
miles.​ (Assume the life spans of the tires have a​ bell-shaped distribution.)
 
 
 

Question content area bottom

Part 1
​(a) The life spans of three randomly selected tires are
33,000
​miles,
36,000
​miles, and
31,000
miles. Find the​ z-score that corresponds to each life span.
 
For the life span of
33,000
​miles, z-score is
negative 0.49
 
−0.49.
​(Round to the nearest hundredth as​ needed.)
Part 2
For the life span of
36,000
​miles, z-score is
0.98
 
0.98.
​(Round to the nearest hundredth as​ needed.)
Part 3
For the life span of
31,000
​miles, z-score is
negative 1.46
 
−1.46.
​(Round to the nearest hundredth as​ needed.)
Part 4
According to the​ z-scores, would the life spans of any of these tires be considered​ unusual?
 
 
Yes
 
No
Your answer is correct.
Part 5
​(b) The life spans of three randomly selected tires are
29,900
​miles,
38,100
​miles, and
34,000
miles. Using the empirical​ rule, find the percentile that corresponds to each life span.
 
The life span
29,900
miles corresponds to a percentile of
enter your response here
 
.
The life span
38,100
miles corresponds to a percentile of
enter your response here
 
.
The life span
34,000
miles corresponds to a percentile of
enter your response here
 
.
​(Round to the nearest whole number as​ needed.)
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