Suppose the length of time it takes college students to find a parking spot on c

Question

Suppose the length of time it takes college students to find a parking spot on campus follows a normal distribution with a mean of 5.2 minutes and a standard deviation of 0.9 minutes. Find the interquartile range of the length of time that a randomly selected college student will find a parking spot on campus. A. 1.21 minutes B. 1.80 minutes C. 5.2 minutes D. None of the answers is correct. Find the probability that a randomly selected college student will NOT find a parking spot within 5.3 minutes. A. 0.456 B. 0.44 C. 0.544 D. 0.956 Suppose a major manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 280 fax machines, 5% arc found to be defective. What is the appropriate alternative hypothesis? A. Ha: p lessthanorequalto .05 B. Ha: p

Explanation / Answer

Mean ( u ) =5.2
Standard Deviation ( sd )=0.9
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
Q1.
P ( Z < x ) = 0.25
Value of z to the cumulative probability of 0.25 from normal table is -0.674
P( x-u/s.d < x - 5.2/0.9 ) = 0.25
That is, ( x - 5.2/0.9 ) = -0.67
--> x = -0.67 * 0.9 + 5.2 = 4.593                  
P ( Z < x ) = 0.75
Value of z to the cumulative probability of 0.75 from normal table is 0.674
P( x-u/s.d < x - 5.2/0.9 ) = 0.75
That is, ( x - 5.2/0.9 ) = 0.67
--> x = 0.67 * 0.9 + 5.2 = 5.807                  

Interquartile range = Q3 - Q1 = 5.807 - 4.593 = 1.21 minuets
Q2.
P(X < 5.3) = (5.3-5.2)/0.9
= 0.1/0.9= 0.1111
= P ( Z <0.1111) From Standard Normal Table
= 0.544                  

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