Question

HELP!!!

The graph shows the normal distribution of the length of similar components produced by a company with a mean of 5 centimeters and a standard deviation of 0.02 centimeters. If a component is chosen at random, the probability that the length of this component is between 4.98 centimeters and 5.02 centimeters is about % and the probability that the length of this component is between 5.02 centimeters and 5.04 centimeters is about %.

Answer 1

1) 68.3%

2)33.3%

Explanation:

Given:

mean, x= 5 cm

Standard deviation, sd= 0.02 cm

probability that the length of this component is between 4.98 centimeters and 5.02 centimeters=?

probability that the length of this component is between 5.02 centimeters and 5.04 centimeters is =?

As the graph shows the normal distribution

a component is chosen at random, the probability that the length of this component is between 4.98 centimeters and 5.02 centimeters is about:

1 sd on either side of the mean on normal distributed graph means

P(|z|<1)

=2(0.3418)

=0.683

=68.3%

the probability that the length of this component is between 5.02 centimeters and 5.04 centimeters is about:

=P(1<z<2) (since between 1 and 2 std dev from the mean)

between 1 and 2 sd on either side of the mean on normal distributed graph means

P(1<z<2)

=0.47-0.342

=0.333

=33.3%!