SOLUTION: According to Comapany 1, the average age of Mercedes buyers in the U.S. is 54 years old. Assume that the standard deviation for the age of these buyers is 8.5 years. A random sampl

Algebra ->  Graphs -> SOLUTION: According to Comapany 1, the average age of Mercedes buyers in the U.S. is 54 years old. Assume that the standard deviation for the age of these buyers is 8.5 years. A random sampl      Log On


   

Question 938940: According to Comapany 1, the average age of Mercedes buyers in the U.S. is 54 years old. Assume that the standard deviation for the age of these buyers is 8.5 years. A random sample of 38 Mercedes buyers was selected. What is the probability that the average age of these buyers is less than 56 years old?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Parameters: mean = 54, SD = 8.5
Sample n = 38
z+=blue+%28x+-+54%29%2Fblue%288.5%2Fsqrt%28n%29%29
p(xbar < 56) = P( z < 2%2F%288.5%2Fsqrt%2838%29%29 = normalcdf(-100,1.7032 )
...
For the normal distribution: Below: z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.
Area under the standard normal curve to the left of 1.7032 = P(1.7032)
Note: z = 0 (x value: the mean) 50% of the area under the curve is to the left and 50% to the right