Question

A company repairs air conditioners. The time it takes to repair them is known to follow a normal distribution that has an average of 14 minutes and a standard deviation of 8.3 minutes. Find the probability that your air conditioner will be repaired in 20.2914 minutes. You can use EXCEL, TI, R or the Table to answer this question. Select one:

a The probability that the air conditioning will be repaired in 20.3 minutes is 95%

b. The probability that the air conditioning will be repaired in 20.3 minutes is 70%

c. The probability that the air conditioning will be repaired in 20.3 minutes is not determinable with the information provided.

d. The probability that the air conditioning will be repaired in 20.3 minutes is 30%

e. The probability that the air conditioning will be repaired in 20.3 minutes is 50%

Answer 1

From the given information,

As the distribution is normal which is continuous,

Then probability that continuous random variable taking a particular value is always zero.

Hence,

P(X=20.2914)=0

We can say like,

P(X<20.2914)=0.78

Hence,

From the given options, the correct answer is,

c. The probability that the air conditioning will be repaired in 20.3 minutes is not determinable with the information provided.

Thank you.