Answer :
The probability the class average is less than 79 is 0.1587.
What is Normal Distribution ?
- The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1.
- The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation.
Given that,
Normally distributed with a mean μ = 80
sample standard deviation σ = 6
In a class, number of students n = 30 (This may be 36 in ques but we take 30 as mentioned in question )
Let, x = be the individual score
∑x = be the class average
It's given, class average is less than 79.
Now, the probability that the class average is less than 79.
P(∑x < 79) = P( (∑x - μ) / (σ/√n) < (79 - 80) / (6 /√30) )
= P( (∑x - μ) / (σ/√n) < (-1) / 1.09 )
= P( (∑x - μ) / (σ/√n) < -1 ) [Round off the Denominator it gives 1]
we know, Standard normal distribution Z = (∑x - μ) / (σ/√n)
so,
P(∑x < 79) = P( Z < -1 )
By Standard normal distribution table,
P( Z < -1 ) = 0.1587
Hence, the probability the class average is less than 79 is 0.1587.
To read more about Normal Distribution
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