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nikdorinn [45]
3 years ago
5

A set of final examination grades in an introductory statistics course is normally​ distributed, with a mean of 77 and a standar

d 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.)
Mathematics
1 answer:
Shalnov [3]3 years ago
7 0

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 = 77

Standard Deviation, σ = 7

We are given that the distribution of examination grades is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(student scored below 86)

P(x < 86)

P( x < 86) = P( z < \displaystyle\frac{86 - 77}{7}) = P(z < 1.2857)

Calculation the value from standard normal z table, we have,  

P(x < 1.2857) = 0.9007 = 90.07\%

0.9007 is the probability that a student scored below 86 on this​ exam.

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