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The distribution of scores in a exam has a normal distribution with a mean of 82 and a standard deviation of 13. What is the probability that a randomly selected score was less than 80? Enter your answer using decimal notation (and not percentages), and round your result to 2 significant places after the decimal (for example the probability of 0.1877 should be entered as 0.19)

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JeanaShupp

Answer: 0.07

Step-by-step explanation:

Given: Mean : [tex]\mu = 82[/tex]

Standard deviation : [tex]\sigma = 13[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 80

[tex]z=\dfrac{80-82}{13}=−0.15384615384\approx-1.5[/tex]

The P Value =[tex]P(z<-1.5)=0.0668072\approx0.07[/tex]

Hence, the  probability that a randomly selected score was less than 80 =0.07

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