For a language test with normally distriuted scores, the mean was 70 and the standard deviation was 10. Approximately what percentage of test takers scored a 60 or above?
Accepted Solution
A:
Answer: 84.13%Step-by-step explanation:Given : The scores in a a language test with normally distributed.Mean : [tex]\mu=70[/tex]Standard deviation: [tex]\sigma= 10[/tex]Let x be the random variable that represents the scores of students.Formula for z-score: [tex]z=\dfrac{x-\mu}{\sigma}[/tex]For x= 60 , we have[tex]z=\dfrac{60-70}{10}=-1[/tex]The probability f test takers scored a 60 or above :-[tex]P(x\geq60)=P(\geq-1)=1-P(z<-1)\\\\=1-0.1586553=0.8413447\approx84.13\%[/tex]Hence, the percentage of test takers scored a 60 or above = 84.13%