Question

Suppose that blood chloride concentration (mmol/L) has a normal distribution with mean 105 and standard deviation 5 What is the probability that chloride concentration equals 106? Is less than 106? Is at most 106? (Round your answers to four decimal places.) equals 106 less than 106 at most 106 (a) 0.5793 05793 (b) What is the probability that chloride concentration differs from the mean by more than 1 standard deviation? (Round your answer to four decimal places.) 0 3174 Does this probability depend on the values of and o? No v , this probability doesnot depend on the values of and ơ. (c) How would you characterize the most extreme 0.8% of chloride concentration values? (Round your answers to two decimal places.) The most extreme 0.8% of chloride concentrations values are those less than 11705 x mmol/L and greater than 11705 X mmol/L You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read ItTalk to a Tutor

can you do problem (c)?

Answer 1

Solution:- The normal distribution is symmetric about it mean
=> The probabilites P(X < c1) = 0.0004, P(X > C2) = 0.0004

The 0.04th and the 99.06th percentile of the standard distribution are -3.35 and 3.35

Hence,

c1 = mu + (Z*sigma)
= 105 + (-3.35*5)
= 88.25

c2 = mu + (Z*sigma)
= 105 + (3.35*5)
= 121.75

The most extreme 0.8% of chloride concentrations value are those less than 88.25 mmol/L and greater than 121.75 mmol/L