Question

Solve two different ways, DO NOT USE NORMAL TABLE

4) The lifetime in hours) of a certain type of light bulb is approximately normal with a mean of 1,000 hours and a standard deviation of 70 hours. What is the probability that the bulb will last between 1050 and 1150 hours? Assume normal distribution. Solve the problem in two (2) completely different ways * 1 way using normal table and 1 way NOT using normal table. (9 marks)

Answer 1

(i) Using Normal Table:

X follows a Normal distribution with mean = 1000 and S.D = 70 Then z=(x-mean)/SD = (x-1000)/70 follows standard Normal. When x=1050, z=(1050-1000)/70 = 0.71 P(Z<0.71) =0.7611 [using Normal table or Excel : NORM.S.DIST(0.71, TRUE)] When x=1150, z=(1150-1000)/70 = 2.14 P(Z<2.14) =0.9838 [using Normal table or Excel : NORM.S.DIST(2.14, TRUE)] P(1050 < X<1150 ) = P(0.71 <Z< 2.14 ) = P(Z < 2.14) - P(Z <0.71 ) = 0.9838 -0.7611 = 0.2227

(ii) Without using Normal table

2ND+VAR --> normalcdf

TI-84 Plus TEXAS INSTRUMENTS normalcdi lower: 1050 upper: 1150 .: 1000 0:70

TI-84 Plus TEXAS INSTRUMENTS normalcdf (1050, .2214629597

Ans : 0.2215