Statistics

For a hypothetical normal distribution of test scores, approximately 95% fall between 38 and 62, 2.5% are below 38, and 2.5% are above 62. Given this information, (a) the mode=_____ and (b) the standard deviation=_____

Thanks in advance!

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  1. To find the mean (this is also the mode):
    (38 + 62)/2 = 50

    95% equals 2 standard deviations about the mean. Therefore, to find 1 standard deviation:
    (50 - 38)/2 = 6
    ...or...
    (62 - 50)/2 = 6

    I hope this helps.

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  2. Thank you very much! I am having real problems with that. Is that the formula that should be used:

    ơ=√∑ (x- µ)2/N

    ?

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