Question

What proportion of Z-scores are outside the interval Z = −2.81 and Z = 2.81?

For Normally distributed data with μ=209.2 and σ=0.6. 31% of observations have values less than______ ?

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 225.1-cm and a standard deviation of 1.3-cm. Suppose a rod is chosen at random from all the rods produced by the company. There is a 33% probability that the rod is longer than:?

Answer 1

Solution :

Given that ,

= P( -2.81 < z < 2.81 )

= P( z < 2.81 ) - P (z < -2.81)

Using z table,

= 0.9975 - 0.0025

= 0.9950

Proportion = 0.9950

Given that,

mean = = 209.2

standard deviation = = 0.6

The z distribution of the  31% is

P( Z < z ) = 31%

P ( Z< z) = 0.31

P( Z < -0.496 ) = 0.31

z = -0.496

Using z-score formula,

x = z * +

x = -0.496 * 0.6 + 209.2

x = 208.90

Answer = 208.90

( A )

Given that ,

mean = = 225.1

standard deviation = = 1.3

The z distribution of the  33% is

( Z > z ) = 33%

P(Z < z ) = 0.33

P ( Z < -0.440 ) = 0.33

Using z-score formula,

x = z * +

x = -0.440 * 1.3 + 225.1

x = 224.528

Answer = 224.53