Question

a normally distributed data has a mean of 0 and standard deviation of 0.5

what is the closest percentage of values between -1 and 1?

A) 34%

B)50%

C)68%

D)95%

Answer #1

Solution :

Given that ,

mean = = 0

standard deviation = = 0.5

P(-1 < x < 1) = P((-1 - 0)/ 0.5) < (x - ) / < (1 - 0) / 0.5) )

= P(-2 < z < 2)

= P(z < 2) - P(z < -2)

= 0.9772 - 0.0228

= 0.9544

=0.95

= 95%

The closest percentage of values between -1 and 1 is 95%

The option D is correct.

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