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Brown eyes
Lv 5
Brown eyes asked in Science & MathematicsMathematics · 6 years ago

Do the width and /or height of a normal distribution change when its standard deviation remains the same but its means decreases?

Update:

The width of a normal distribution curve (increase, decrease, remains the same) and its height (increase, decrease, remains the same) when its standard deviation remains the same but its means decreases. Can you tell me what to choose, I am confused.

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  • Michael
    Lv 7
    6 years ago

    Well,

    what do you mean by "width" ? the domain is (-oo, +oo) ... ;-)

    ==> the answer is NO : the shape of the normal curve remains unchanged after a shift of mean

    wanna know why ?

    because the function is (for a N(µ , σ) meaning : mean = µ, std dev. = σ )

    f(x) = (1/ (σsqrt(2pi) ) * e^( - (x - µ)^2/ (2σ^2) )

    and what do we see ?

    ==> the function is a function of (x - µ)

    hope it' ll help !!

  • Brown eyes
    Lv 5
    6 years ago

    Thanks for your answer. I found the answer, the answer is it remains the same

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