Question

ILLEBuus Ilds un that customers become unhappy if they love to more than five times, what do you infer about the customer satisfaction with the above IVRS system? : (a) An analysis of inpatient data in a hospital revealed that the number of days that admitted patients spend in the hospital has a normal distribution with a mean of four days and standard deviation of one day. (1) What proportion of inpatients spend atleast five days in that hospital? (ii) What is the maximum number of days spent by 30% of inpatients who stay for lesser duration in the hospital? (b) Parts and Materials for laboratory equipment in a medical college are supplied by two suppliers. Supplier A's materials make up 30% of what is used, with supplier B providing the rest. Past records indicate that 5% of supplier A's materials are defective and 3% of B's are defective. Since it is impossible to tell which supplier the materials came from once they are in inventory, the pathologist wants to know which supplier most likely Do not write on the question paper. Please go on to the next page... Scanned with CamScanner

Answer 1

Answer to part a)

Part ( i )

Mean ( M ) = 4

Standard deviation ( SD ) = 1

.

To find P(at least 5 days) = 1 - P(less than 5 days)

z = (x - M) / SD

x = 5, M = 4, SD = 1

On plugging the values we get

z = (5 -4 )/1 = 1

P(z < 1) = 0.8413 [ from Z table]

P(at least 5) = 1 - 0.8413

P(at least 5) = 0.1587

Thus 15.87% of patients spend atleast 5 days

.

Part (ii)

Lowest 30%

Z value for p = 0.30

z = -0.5244 [ from Z table or excel function = normsinv(0.30) ]

.

Using Z formula

Z = (x - M) / SD

-0.5244 = (X - 4) / 1

X = 4-0.5244

X = 3.4756 ~ 3 days

Thus lowest 30% patients spend maximum 3 days