Answer:
The probability of obtaining a score less than 60 is 2.28%
It happens 2 out of 100 times.
Step-by-step explanation:
If the mean μ = 80 and the standard deviation σ = 10, then we need to find the probability that an X value is less than 60.
Then we find
[tex]P(X <60)[/tex]
To find this probability we use the Z statistic.
[tex]Z = \frac{X- \mu}{\sigma}[/tex]
[tex]P(\frac{X- \mu}{\sigma}<\frac{60-80}{10})[/tex]
[tex]P(Z <-2)[/tex]
This is the same as
[tex]P(Z> 2)[/tex]
We look for this value in the table for the normal distribution of right queue and we have:
[tex]P(X <60) = P(Z> 2) = 0.02275[/tex]
The probability of obtaining a score less than 60 is 2.28%
It happens 2 out of 100 times.
