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Math Help - Solving problem involving normal distributions

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    Solving problem involving normal distributions

    Asiah found that the time taken to travel from her house to her office is normally distributed with a mean of 40 minutes and a varience of 64 minutes^2.If she leaves home at 7:30am,Find the probability that she will arrive after 8:15 am


    please help
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    Transform it to the standard Z distribution and look it up on your normal probability tables...
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    Quote Originally Posted by mastermin346 View Post
    Asiah found that the time taken to travel from her house to her office is normally distributed with a mean of 40 minutes and a varience of 64 minutes^2.If she leaves home at 7:30am,Find the probability that she will arrive after 8:15 am


    please help
    \sigma^2=64\Rightarrow\sigma=+\sqrt{64}=8\;\text{\  footnotesize\ minutes}

    You want the probability that the time taken is >45 minutes...

    therefore, you require

    P\left(Z>\frac{x-\mu}{\sigma}\Rightarrow\ Z>\frac{45-40}{8}\right)
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    thanks archie meade

    how about this..
    In standard sports of a school,all students took part in the 100m race.The time taken to finish the race by a Form 2 student in normally distributed with a mean of 15 seconds and variance of 25 seconds^2.For a student who took less than 16 seconds,1 mark was awarded and for one who took less than 14 seconds,2 marks were awarded.

    a)find the percentage of Form 2 students who got 1 mark each.

    b)Find the number of Form 2 students who got 2 marks if 200 Form 2 students took part.
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    Quote Originally Posted by mastermin346 View Post
    thanks archie meade

    how about this..
    In standard sports of a school,all students took part in the 100m race.The time taken to finish the race by a Form 2 student in normally distributed with a mean of 15 seconds and variance of 25 seconds^2.For a student who took less than 16 seconds,1 mark was awarded and for one who took less than 14 seconds,2 marks were awarded.

    a)find the percentage of Form 2 students who got 1 mark each.

    b)Find the number of Form 2 students who got 2 marks if 200 Form 2 students took part.
    (a)

    Again, the question gives the variance, so the standard deviation is the square root of that...

    \sigma=+\sqrt{25}=5

    \mu=15

    Z=\displaystyle\frac{x-\mu}{\sigma}=\frac{16-15}{5}=0.2

    Therefore, you need to find

    P(Z<0.2)

    The percentage of students who got one mark is then 100 times the probability
    of a student finishing the race in less than 16 seconds.

    Try that and then maybe (b) is do-able.
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