SOLUTION: Here's another that i think i know how to do, but am not really sure. please help me out!!! A statistical analysis of 1,000 long distance telephone calls made from the headquart

Question 21657: Here's another that i think i know how to do, but am not really sure. please help me out!!!
A statistical analysis of 1,000 long distance telephone calls made from the headquarters of the Bricks and Clicks Computer Corporation indicates that the length of these calls is normally distributed with m = 240 seconds and s = 40 seconds.
a) What is the probability that a call lasts less than180 seconds?
b) What is the probability that a particular call lasts between 180 and 300 seconds?
c) What is the length of a call if only 1% of all calls are shorter?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
A statistical analysis of 1,000 long distance telephone calls made from the headquarters of the Bricks and Clicks Computer Corporation indicates that the length of these calls is normally distributed with m = 240 seconds and s = 40 seconds.
a) What is the probability that a call lasts less than180 seconds?
b) What is the probability that a particular call lasts between 180 and 300 seconds?
c) What is the length of a call if only 1% of all calls are shorter?
WE DO IT BY USING NORMAL DISTRIBUTION FORMULAE
MEAN=M=240......STANDARD DEVIATION =S=40... X IS THE VALUE UNDER CONSIDERATION..
1.X<180..SAY X=180...T=(X-M)/S=(180-240)/40=-1.5..NOW WE FIND PROBABILITY DENSITY FUNCTION FOR THIS VALUE OF T.......F(-1.5)=0.5-F(1.5)..WE FIND FROM TABLES THAT F(1.5)=0.4332..HENCE PROBABILITY THAT CALL LASTS LESS THAN 180 SECS IS
0.5-0.4332=0.0668.
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2.180 X=300.........T=(300-240)/40=1.5.............F(1.5)=0.4332
SO WE WANT AREA UNDER F(-1.5) TO F(1.5)=2*0.4332=0.8664
HENCE PROBABILITY OF THE CALL LASTING BETWEEN 180 AND 300 SECS IS 0.8664
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3.1% OF ALL CALLS ARE SHORTER...PROBABILITY =0.01...AREA UNDER STD.CURVE ....
0.5-0.01=0.49.....CORRESPONDING VALUE OF T IS -2.33
HENCE -2.33=(X-240)/40
X-240=-93.2...X=146.8 SECS.
HENCE LENGTH OF CALL IS LESS THAN 146.8 SECS FOR 1 % OF CALLS
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