For certain workers, the mean wage is $5.00/hr, with a standard deviation of $0.25. If a worker is chosen at random, what is the probability that the workers wage is between $4.25-$5.75. Assume a normal distribution of wages.
Accepted Solution
A:
Answer:P(-3.0 < z < 3.0) = 0.9974Step-by-step explanation:Mean = 5Standard Deviation = 0.25We need to find P(4.25 <x<5.75)z = x - mean/standard deviationz = 4.25 - 5/0.25z = -3.0z = x - mean/standard deviationz = 5.75 - 5/0.25z = 3.0So, P(4.25 <x<5.75) P(-3.0 < z < 3.0)Finding values from the z-score tableP(z<-3.0) = 0.0013P(z<3.0) = 0.9987P(-3.0 < z < 3.0)=P(z<3.0) - P(z<-3.0) P(-3.0 < z < 3.0) = 0.9987 - 0.0013P(-3.0 < z < 3.0) = 0.9974