Question

Use the following info for 17-19. A normally distributed data set has a mean of 100 and a standard deviation of 10. 17. What percentage of values are greater than 90? 18. What percentage of values are less than 90? 19. What z score corresponds to a value of 110? 20. What z score corresponds to a value of 90

Answer 1

Solution :

Given ,

mean = $\mu$ $\mu$ = 100

standard deviation = $\sigma$ = 10

P(x >90 ) = 1 - P(x<90 )

= 1 - P[(x -$\mu$) / $\sigma$ < (90-100) /10 ]

= 1 - P(z <-1 )

Using z table

= 1 - 0.1587

= 0.8413

=84.13%

18.

P(x<90 )

= P[(x -$\mu$) / $\sigma$ < (90-100) /10 ]

= P(z <-1 )

Using z table

=0.1587

= 15.87%

19.

using z score formula

z=(x -$\mu$) / $\sigma$

z= (110-100) /10

z=1

20.

z=(x -$\mu$) / $\sigma$

z= (90-100) /10