A random variable x is normally distributed with a mean of 100 and a variance of 25. Given that x = 110, its corresponding z- score is 0.40.
Answer: The given z-score is false.
Explanation: We are given:
Mean, [tex]\mu=100[/tex],
Variance, [tex]\sigma^{2}=25[/tex]
[tex]\therefore\sigma=\sqrt{\sigma^{2}}[/tex]
[tex]=\sqrt{25}[/tex]
[tex]=5[/tex]
The z-score formula is given below:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]=\frac{110-100}{5}[/tex]
[tex]=\frac{10}{5}[/tex]
[tex]=2[/tex]
Therefore, the z-score corresponding x=100 is 2
Therefore, the given z-score = 0.4 is false.
