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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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================================================

Explanation:

The number 245 is a natural number since the set of natural numbers is {1, 2, 3, 4, 5, 6, ...} basically the set of counting numbers. More technically, the set of natural numbers is the set of positive whole numbers.

The number 245 is also an integer. It does not have any decimal or fractional parts. The set of integers includes negative whole numbers as well.

The number 245 is a whole number for similar reasoning as it being an integer.

The number 245 is a rational number. Why? Because we can write 245 as 245/1. In other words, 245 = 245/1. Because we can form a fraction of two integers, this shows us 245 is rational. Note: 0 cannot be in the denominator.

The number 245 is NOT an irrational. If a number is rational, then it cannot be irrational. The very definition of "irrational" means "not rational". An example of an irrational number is sqrt(2). We cannot write this as a fraction of two integers.

The number 245 is a real number. If you haven't learned about complex numbers yet, then every number you encounter is a real number.

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To summarize, 245 is a natural number, a whole number, an integer, a rational number, and a real number.

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