Question

From 25 samples, each with size 10, you estimated that the hospital’s EHR downtime average time was 30 minutes with the standard deviation of 2 minutes. Your process is assumed stable and normally distributed.

(a) What is the potential capability of the system to meet the specifications of ??? = 10 minutes and ? ?? = 45 minutes?

(b) What is the actual capability of the system to meet the specifications of ??? = 10 minutes and ? ?? = 45 minutes?

(c) What is the percentage the allowed bandwidth is the process using?

(d) What is the probability of observing a downtime period longer than 45 minutes?

Answer 1

Part A:

Formula:

So,

P_p = (45 - 10)/(6*2)

Or,

P_p = 2.92

Part B:

= Minimum of {(45 - 30)/(3*2), (30 - 10)/(3*2)}

= Minimum of (2.5, 3.3333)

= 2.5

Part C will be uploaded soon...

Part D:

As the sample size is 25 (less than 25), so we will use t test in this regard..

Or,

t = (45 - 30)/(2/25^1/2)

Or,

t = 37.5

Here, degree of freedom = 25 -1 = 24

So, the corresponding P value is less than 0.0005

So, the probability of observing a downtime period longer than 45 minutes = 1 - 0.000005 = 0.9999

Refer the t table given below to get a clarity on the P value:

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