Answer: 0.2789
Step-by-step explanation:
Given: Mean : [tex]\mu=10.00\ mm [/tex]
Standard deviation : [tex]\sigma =0.03\ mm[/tex]
The formula to calculate z-score is given by :_
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 9.96 mm, we have
[tex]z=\dfrac{10-9.96}{0.03}\approx1.33[/tex]
For x= 10.01 mm, we have
[tex]z=\dfrac{10.01-10}{0.03}\approx0.33[/tex]
The P-value = [tex]P(0.33<z<1.33)=P(z<1.33)-P(z<0.33)[/tex]
[tex]= 0.9082408- 0.6293=0.2789408\approx0.2789[/tex]
Hence, the probability that a randomly selected gear has a diameter between 9.96 mm and 10.01 mm =0.2789
Answer:
Pr=0.2894
Step-by-step explanation:
given mean diameter =10 mm
standard deviation=0.03 mm
z equation is
z=x-μ/σ
The problem has two values of x
for x=9.96
z=-1.33
for x-10.01
z=0.33
from Probability table we have
Pr(-1.33<z<0.33)=pr(z<0.33)-pr(z>-1.33)
Pr=0.2894
