Public health and nutrition. Emergency defibrillators are now located in many pu

Question

Public health and nutrition. Emergency defibrillators are now located in many public buildings. However, the U.S. Food and Drug Administration (FDA) is concerned about the reliability of these devices. Approximately 45,000 devices failed during the past seven years. Suppose the FDA claims that the probability of an emergency defibrillator working correctly is 0.9 , and 32 of these devices are selected at random and tested.

(a) Find the probability (±0.0001) that exactly 27 devices will work correctly.?

P(X=27) =

(b) Find the probability (±0.0001) that at least 26 devices will work correctly?

P(X26) =

(c) Suppose only 19 of the devices work correctly. Is there any evidence to suggest that the proportion of emergency defibrillators that work correctly has changed??

P(X19) (±0.0001) =

Conclusion:

There is evidence to suggest the claim is false

There is no evidence to suggest the claim is false

There is evidence to suggest the claim is false

There is no evidence to suggest the claim is false

Explanation / Answer

Given , probability of workig correctly P =0.9;Number selected at random 'n' =32

so Q=1-0.9 =0.1

Assume 'X' is the number working correctly follows binomial distribution with P=0.9, n =32, Q=0.1

a) The probability (±0.0001) that exactly 27 devices will work correctly is P(X=27) = =BINOMDIST(27,32,0.9,0)=0.1171

(b) The probability (±0.0001) that at least 26 devices will work correctly is P(X>=26) = 1-P(X<=25)

=1-BINOMDIST(25,32,0.9,25)=1-0.0358=0.9642

c) If 19 are working correctly then p =19/32 = 0.5938

Null hypothesis : There is no change in proportion; Alternative hypothesis: There is change in proportion.

To test the claim, the test statistic z = (p-P)/SE; Where SE = sqrt(P*Q/n) = sqrt(0.9*0.1/32)=0.0530

so z =(0.5938-0.9)/0.0530 = -5.77

We reject the null hypothesis.

There is no evidence to suggest the claim is false

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