Question

a.) A sample set is normally distributed with a mean of 2.8 and a standard deviation of 0.7. Approximately, what percentage of the sample is between the values of 2.1 and 3.5?

b.) A sample set is normally distributed with a mean of 66 and a standard deviation of 8.
Find a z-score corresponding to a given value of 82.

Answer 1

Solution :

Given that ,

mean =   = 2.8

standard deviation = = 0.7  

P(2.1< x <3.5 ) = P[(2.1-2.8) /0.7 < (x - ) / < (3.5-2.8) / 0.7)]

= P( -1< Z < 1)

= P(Z <1 ) - P(Z <-1 )

Using z table   

= 0.8413-0.1587

=0.6826

answer =68.26%

(B)olution :

Given ,

mean = = 66

standard deviation =   = 8

x=82

using z-score formula

z =X -/

z=82-66/8

z=2