Suppose the ages of employees at the Dr Pepper Snapple Bottling Company follow a

Question

Suppose the ages of employees at the Dr Pepper Snapple Bottling Company follow an approximate normal distribution with a mean of 42.2 years and a standard deviation of 7.8 years. Use this information to answer question 5. Please circle your final answer. 5. Chnar and Rommy both work for the Dr Pepper Snapple Bottling Company; Chnar is 30 years old, while Rommy is 51 years old. Based on the distribution described above, what is the probability that the age of an employee will be between 30 and 51 years old? (7 pts)

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 42.2
standard Deviation ( sd )= 7.8
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 30) = (30-42.2)/7.8
= -12.2/7.8 = -1.5641
= P ( Z <-1.5641) From Standard Normal Table
= 0.0589
P(X < 51) = (51-42.2)/7.8
= 8.8/7.8 = 1.1282
= P ( Z <1.1282) From Standard Normal Table
= 0.8704
P(30 < X < 51) = 0.8704-0.0589 = 0.8115

the probablity that the age of the employee between 30 and 51 is 0.8115

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