Please I need help on this problem After 1000 measurements of some quantity x, t

Question

Please I need help on this problem

After 1000 measurements of some quantity x, the mean value x and the standard deviation ? are determined to be 30 and 4, respectively.

a)  What is the probability that measurement number 1001 is greater than 34?

b)  What is the probability that measurement number 1001 is greater than 25 but

less than 30?

After 1000 measurements of some quantity x, the mean value x and the standard deviation ? are determined to be 30 and 4, respectively. What is the probability that measurement number 1001 is greater than 34? What is the probability that measurement number 1001 is greater than 25 but less than 30?

Explanation / Answer

1. Probability that measurement number 1001 is greater than 34= 1- (probability that measurement number 1001 is lesser than 34 )= 1- (area to the left of mean + area from mean to (mean + standard deviation i.e t=1))

= 1- (0.5+0.3413) = 0.1587

2.Probability that measurement number 1001 is greater than 25 but less than 30

Hence required probability = (area from 26 to 30 )

= area from 30 to 34

=0.3413

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