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nickersia

  • 2 years ago

A random variable X follows a normal distribution with mean 20. (standard deviation 5) Find probability 14=<X=<26

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  1. nickersia
    • 2 years ago
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    \[14 \le x \le 26\]

  2. kropot72
    • 2 years ago
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    Do you know how to work out the z-scores for 14 and 26? \[z=\frac{X-\mu}{\sigma}\]

  3. nickersia
    • 2 years ago
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    Yes, but I'm not sure should I put 6 and -6 for z? That way I got 50 for x, which makes me no sense

  4. kropot72
    • 2 years ago
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    \[z _{1}=\frac{14-20}{5}=?\] \[z _{2}=\frac{26-20}{5}=?\]

  5. nickersia
    • 2 years ago
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    I got 76.98% as an answer. z= -1.2 and 1.2 So, z score from beginning of the curve to the s.d. of 1.2 is 0.8849, which meas that on the right it's 0.1151 and same on the left, so it's 0.2302. 23.02% are lower than 14 and bigger that 26, so 76.98% is X. Am I right?

  6. kropot72
    • 2 years ago
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    A standard normal distribution table gives the following values for cumulative probability: z = 1.2 : p = 0.8849 z = -1.2 : p = 0.1151 You can check these results on the table at the following link (choose 'normal.pdf' from the menu: http://www.math.bgu.ac.il/~ngur/Teaching/probability/

  7. kropot72
    • 2 years ago
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    \[P(14<X <26)=0.8849-0.1151=?\]

  8. nickersia
    • 2 years ago
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    0.7698 which is 76.98% So, I suppose I got it right :) That's basically the same thing I did, thank you very much! :)

  9. kropot72
    • 2 years ago
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    You're welcome :)

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