Question

(1 point) Assume that the readings on the thermometers are normally distributed with a mean of 0° and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. Find the probability of each reading in degrees. (a) Between 0 and 1.9. (b) Between -2.54 and 0 (C) Between -0.98 and 0.06 (d) Less than -2.76 (e) Greater than -0.94:

Answer 1

Part a)

P ( 0 < Z < 1.9 ) = P ( Z < 1.9 ) - P ( Z < 0 )
P ( 0 < Z < 1.9 ) = 0.9713 - 0.5
P ( 0 < Z < 1.9 ) = 0.4713

part b)

P ( -2.54 < Z < 0 ) = P ( Z < 0 ) - P ( Z < -2.54 )
P ( -2.54 < Z < 0 ) = 0.5 - 0.0055
P ( -2.54 < Z < 0 ) = 0.4945

Part c)

P ( -0.98 < Z < 0.06 ) = P ( Z < 0.06 ) - P ( Z < -0.98 )
P ( -0.98 < Z < 0.06 ) = 0.5239 - 0.1635
P ( -0.98 < Z < 0.06 ) = 0.3604

Part d)

P ( Z < -2.76 ) = 0.0029

Part e)

P ( Z > -0.94 ) = 1 - P ( Z < -0.94 )
P ( Z > -0.94 ) = 1 - 0.1736
P ( Z > -0.94 ) = 0.8264