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arp x y @ Do Homework-Patrok : At One Point The Averag X Post University l Online C Secure https://www tudent/PlayerHomeworkaspxžhomeworkld-5014609618&questionld-5&flushed-false&cld-520. Patrick Howard&1 9/5/18 9:09 MAT220.30: Statistics I [MOD1 ONLINE(8/27-10/21/2018)] Homework: UNIT 2 -Section 3.2 Homework Score: 0 of 1t 332.35 5 of 5 (5 complete) HW Score: 51.43%, 2.57 of Question Help At one point the average price of regular unloaded gasoline was $3 64 per galon Assume that the standard deviation price per galon is S0 04 per gallon and use Chebyshev's inequality to answer the tolilowing (a) What percentage of gasoline stations had prices within 2 standard deviations of the mean? (b) What percentage of gasoline stations had prices within 1 5 standard deviations of the mean? What are the gasoline prices that are within 1.5 standard deviations of the mean? (c) What is the minimum percentage of gasoline stations that had prices between $3.52 and $3.76? a) At least y of gasoline stations had prices within 2 standard deviations of the mean Round to two decimal places as needed)Explanation / Answer
(a)
It is given that the average price of regular unleaded gasoline was $3.64 per gallon.
That is, = $3.64
The population standard deviation, =$0.04 per gallon.
According to Chebyshev's inequality,
P[(|X - |)< k] >= 1 - (1/k^2)
P[(X - |) < 2] >= 1 - (1/2^2)
>= 1 -(1/4)
>= 0.75
The percentage of gasoline stations had prices within 2 standard deviations of the mean is 75%
So,
At least 75% of gassoline stations had prices within 2 standard deviatins of the mean.
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