Question

The widths of platinum samples manufactured at a factory are normally distributed, with a mean of 1.1 cm and a standard deviation of 0.1 cm. Find the z-scores that correspond to each of the following widths. Round your answers to the nearest hundredth, if necessary.

(a) 1.6 cm

z =

(b) 0.2 cm

z =

Answer 1

Solution :

Given that ,

mean = = 1.1

standard deviation = = 0.1

(a ) P(x < 1.6 ) = P[ ( x - ) / < ( 1.6 - 1.1 ) / 0.1 ]

= P( z < 5 )

The z - scores = 5.00  

( b )

P( x < 0.2) = P[( x - ) / < ( 0.2 - 1.1 ) / 0.1]

= P ( z < -9 )

The z - score = -9.00