The temperature recorded by a certain thermometer when place

The temperature recorded by a certain thermometer when placed in boiling water (true temperature 100 degree C) is normally distributed with mean p=99.8 degree C and standard deviation sigma =1-1 degree C. a) What is the probability that the thermometer reading is greater than 100 degree C? b) What is the probability that the thermometer reading is within +- 0.05 degree C of the true temperature? c) What is the probability that a random sample of 30 thermometers has a mean thermometer reading is less than 100 degree C? (inclusive)

Solution

mean mu=99.8

standatd devaition d=1.1

a. P( reading greater than 100)=P( X >100)

                             =P( Z > (100-99.8)/1.1)

                          =P( Z > 0.1818)

                               = 0.42 79   from standard normal table

b) P( |X-mu | < 0.05) =P(-0.05 < X -mu< 0.05)

                             = P( (-0.05/1.1 < Z < 0.05/1.1)

                            =0.0363

c) mean od Xbar =99.8

sd of Xbar= 1.1/sqrt(3)

P( Xbar < 100)= P( Z < (100-99.8)/(1.1/sqrt(30))

                          =P( Z < 0.9959)

                       =0.8404