Question

The length of similar components produced by a company is approximated by a normal distribution model with a mean of $5$ cm and a standard deviation of $0.02$ cm. If a component is chosen at random .what is the probability that the length of this component is between $4.98$ and $5.02$ cm?

• A. $0.5826$
• B. $0.6826$
• C. $0.6259$
• D. $0.6598$

Answer 1

The correct option is B $0.6826$

Given,

$\mu =5$(mean)

$\sigma =0.02$ (standard deviation)

find the probability for $4.98<x<5.02$

converting the problem in standard form

$Z=(x-\mu )/\sigma$

for $x=4.98$,

$Z=-1$

for $x=5.02$,

$Z=1$

for finding the probability for $4.98<x<5.02$

in the standard form $-1<z<1$

in standard form mean is equal to zero and the standard deviation is 1.

ao we will have find the probability for $(\mu -\sigma )$ to$(\mu +\sigma )$

i.e. $-1to+1$

and probability for $(\mu -\sigma )$ to$(\mu +\sigma )$ is $0.6826$