Question

pH measurements of a chemical solutions have mean 6.8 with standard deviation 0.04. Assuming all pH measurements of this solution follow a normal distribution, find the probability of selecting a pH measurement at random that reads below 6.68 OR above 6.88 without using the LSND program. (Write the answer in decimals)

Answer 1

Solution :

Given that ,

mean = = 6.8

standard deviation = = 0.04

P( x < 6.68 or x > 6.88 )

= 1 - P( 6.68 < x < 6.88)

= 1 - P((6.68 - 6.8)/ 0.04) < (x - ) /  < (6.88 -6.8) / 0.04) )

= 1 - P(-3 < z < 2)

= 1 - (P(z < 2) - P(z < -3))

= 1 - ( 0.9772 - 0.0013 ) Using standard normal table,  

Probability = 0.0241