Question

An sample has a mean of 48 and a standard deviation of 7.6.

(a) Find the z-score for each value of x = 52. (Give your answer correct to two decimal places.) 0.53 (b) Find the z-score for each value of x = 59. (Give your answer correct to two decimal places.) (c) (a) Find the z-score for each value of x = 45. (Give your answer correct to two decimal places.) (d) (a) Find the z-score for each value of x = 43. (Give your answer correct to two decimal places.)

Answer 1

We have given :

An sample has a

mean = 48 and a

standard deviation = 7.6.

we have to find z score value ,

z score = ( x - mean of sample  ) / sample standard deviation  

where x = observed value

## (a) Find the z-score for each value of x = 52. (Give your answer correct to two decimal places.) 0.53

Answer : z = ( 52 - 48 ) / 7.6 = 4 / 7.6 = 0.526315 ie 0.53 ( it is positive )

z score for x = 52 is 0.53

  

##(b) Find the z-score for each value of x = 59. (Give your answer correct to two decimal places.)

Answer :  z = ( 59 - 48 ) / 7.6 = 11 / 7.6 = 1.447368   ie 1.45 ( it is positive)

z score for x = 59 is 1.45

  

## (c) (a) Find the z-score for each value of x = 45. (Give your answer correct to two decimal places.)

Answer :  z = ( 45 - 48 ) / 7.6 = - 3 / 7.6 = - 0.394736 ie - 0.39 ( it is negative )

z score for x = 45 is - 0.39

## (d) (a) Find the z-score for each value of x = 43. (Give your answer correct to two decimal places.)

Answer :  z = ( 43 - 48 ) / 7.6 = - 5 / 7.6 = - 0.657894 ie - 0.66 ( it is negative )

z score for x = 43 is - 0.66