Answer:
z-score = 3.5, Yes, z-score is unusual.
Step-by-step explanation:
Given information:
Population mean ; μ = 6 feet
Standard deviation ; σ = 0.2 feet
Sample mean = 6.7 feet
The formula for z-score is
[tex]z=\dfrac{\overline{X}-\mu}{\sigma}[/tex]
where, [tex]\overline{X}[/tex] is sample mean, μ is population mean and σ is standard deviation.
Substitute the given values in the above formula.
[tex]z=\dfrac{6.7-6}{0.2}[/tex]
[tex]z=\dfrac{0.7}{0.2}[/tex]
[tex]z=3.5[/tex]
The z-score is 3.5.
If a z-score is less than -2 or greater than 2, then it is known as unusual score.
3.5 > 2
It means z-score is unusual.
Since the z score is greater than 3, hence his score is unusual.]
Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\ \\ where\ x=raw\ score,\mu=mean\ and\ \sigma=standard\ deviation[/tex]
Given that mean = 6, standard deviation = 0.2.
For x = 6.7:
[tex]z=\frac{6.7-6}{0.2}=3.5 [/tex]
Since the z score is greater than 3, hence his score is unusual.
Find out more on z score at: https://brainly.com/question/25638875
