Answer:
The probability is 0.977
Step-by-step explanation:
We know that the average [tex]\mu[/tex] is:
[tex]\mu=500[/tex]
The standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=100[/tex]
The Z-score is:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
We seek to find
[tex]P(x>300)[/tex]
The Z-score is:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{300-500}{100}[/tex]
[tex]Z=-2[/tex]
The score of Z = -2 means that 300 is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 1 deviations from the mean has percentage of 2.35% for Z<-2
So
[tex]P(z>-2)=1-P(Z<-2)[/tex]
[tex]P(z>-2)=1-0.0235[/tex]
[tex]P(z>-2)=0.9765[/tex]
