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    The times for a certain car journey have a normal distribution with mean 100 minutes and standard deviation 7 minutes. Journey times are classified as follows:
    ‘short’ (the shortest 33% of times),
    ‘long’ (the longest 33% of times),
    ‘standard’ (the remaining 34% of times).
    (i) Find the probability that a randomly chosen car journey takes between 85 and 100 minutes.
    (ii) Find the least and greatest times for ‘standard’ journeys.

    Sol. (i) I got 0.484 as answer by solving P(85<X<100).
    I am really confused on (ii).
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    (Original post by kundanad)
    The times for a certain car journey have a normal distribution with mean 100 minutes and standard deviation 7 minutes. Journey times are classified as follows:
    ‘short’ (the shortest 33% of times),
    ‘long’ (the longest 33% of times),
    ‘standard’ (the remaining 34% of times).
    (i) Find the probability that a randomly chosen car journey takes between 85 and 100 minutes.
    (ii) Find the least and greatest times for ‘standard’ journeys.

    Sol. (i) I got 0.484 as answer by solving P(85<X<100).
    I am really confused on (ii).
    If we consider 'short' times. These are the shortest 33% of times so if s is the greatest short time then it must be true that

    P(X &lt; s) = 0.33. Does this make sense? And can you use this hint to answer the question?
 
 
 
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