Answer:
The probability is 0.0015
Step-by-step explanation:
We know that the mean [tex]\mu[/tex] is:
[tex]\mu=6:30\ p.m[/tex]
The standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=0:15\ minutes[/tex]
The Z-score is:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
We seek to find
[tex]P(x>7:15\ p.m.)[/tex]
The Z-score is:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{7:15-6:30}{0:15}[/tex]
[tex]Z=\frac{0:45}{0:15}[/tex]
[tex]Z=3[/tex]
The score of Z = 3 means that 7:15 p.m. is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%
So
[tex]P(x>7:15\ p.m.)=P(Z>3)=0.0015[/tex]
