Question

Assume that process that makes the parts can be altered to adjust the overall mean of the reflectiveness score. Also assume that if an individual part has a score less than 85, then the part is given a passing quality score. The adjusted value of the true mean in population S that would result in approximately 80% of parts from that population being given a passing score is:______

a. greater than 80
b. less than 80
c. equal to 80

Answer 1

c. equal to 80

Explanation:

Given that:

The population mean = 80

The standard deviation is = 6

The sample mean = 85

The objective is to find the probability that is less than 85

`P(X < 85) = P( Z < (x-\mu)/(\sigma))`

`P(X < 85) = P( Z < (85-80)/(6))`

`P(X < 85) = P( Z < (5)/(6))`

`P(X < 85) = P( Z < 0.833)`

From the standard normal table

P(X <85) = 0.7977

P(X< 85) = 79.77%

P(X< 85) = 80%

Therefore, The adjusted value of the true mean in population S that would result in approximately 80% of parts from that population being given a passing score is: equal to 80 .