A set of final examination grades in an introductory statistics course is normally​ distributed, with a mean of 77 and a standard deviation of 7. Complete parts​ (a) through​ (d). a. What is the probability that a student scored below 86 on this​ exam? The probability that a student scored below 86 is nothing. ​(Round to four decimal places as​ needed.)

Answer:0.9007 is the probability that a student scored below 86 on this​ exam.Step-by-step explanation:We are given the following information in the question: Mean, μ = 77Standard Deviation, σ = 7We are given that the distribution of examination grades is a bell shaped distribution that is a normal distribution. Formula: [tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]a) P(student scored below 86) P(x < 86) [tex]P( x < 86) = P( z < \displaystyle\frac{86 - 77}{7}) = P(z < 1.2857)[/tex] Calculation the value from standard normal z table, we have,  [tex]P(x < 1.2857) = 0.9007 = 90.07\%[/tex]0.9007 is the probability that a student scored below 86 on this​ exam.