Answer: 0.1841
Step-by-step explanation:
Given: Mean : [tex]\mu=8.2[/tex]
Standard deviation : [tex]\sigma = 1.34[/tex]
The formula to calculate z-score is given by :_
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 9, we have
[tex]z=\dfrac{9-8.2}{1.34}\approx0.60[/tex]
For x= 10, we have
[tex]z=\dfrac{10-8.2}{1.34}\approx1.34[/tex]
The P-value = [tex]P(0.6<z<1.34)=P(z<1.34)-P(z<0.6)[/tex]
[tex]=0.9098773-0.7257469=0.1841304\approx0.1841[/tex]
Hence, the probability that at your next exam, you will have a stress level between 9 and 10 = 0.1841
