Please give me calculator stepsScores on a statistics final in a large class were normally distributed with a mean of 70 and a standard deviation of 7. Find the following probabilities, round to the fourth.a) What is the probability one randomly chosen score is greater than 88Would it be unusual for this to happen?Select an answer not unusual unusual  b) What proportion of scores were below a 45? Would it be unusual for this to happen?Select an answer unusual not unusual

Question
Asked Oct 16, 2019

Please give me calculator steps

Scores on a statistics final in a large class were normally distributed with a mean of 70 and a standard deviation of 7. Find the following probabilities, round to the fourth.
a) What is the probability one randomly chosen score is greater than 88

Would it be unusual for this to happen?
Select an answer not unusual unusual  
b) What proportion of scores were below a 45? 
Would it be unusual for this to happen?
Select an answer unusual not unusual  

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Expert Answer

Step 1

Consider, X be a random variable that represents the score of statistics in a large class is normally distributed with mean (µ) and standard deviation (σ),that is,

X~N(μ =70, σ = 7)
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X~N(μ =70, σ = 7)

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Step 2

a)

The required probability that one randomly selected score is greater than 88 is calculated as:

P(X2 88) 1-P(X < 88)
X-u88-70
_
=1- P
7
1-P(Z <2.57)
(Using standard normal table)
=1-0.994
=0.0051
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P(X2 88) 1-P(X < 88) X-u88-70 _ =1- P 7 1-P(Z <2.57) (Using standard normal table) =1-0.994 =0.0051

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Step 3

Since, the probability is less than 5%. ...

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