Respuesta :
Answer:
(a) The difference between Kate's IQ and the mean is 21
(b) The z score is 1.4
Step-by-step explanation:
Here is the complete question:
IQ scores have a mean of 100 and a standard deviation of 15. Kate has an IQ of 121. (a) What is the difference between Kate's IQ and the mean (b) Convert Kate's IQ score to a z score.
Step-by-step explanation:
(a) To determine the difference between Kate's IQ and the mean, this can be done by subtracting the mean from Kate's IQ.
Mean = 100
Kate's IQ = 121
Difference between Kate's IQ and the mean = 121 - 100 = 21
Hence, the difference between Kate's IQ and the mean is 21.
(b) To convert Kate's IQ score to a z score,
z score is given by the formula
[tex]z =\frac{x - \mu}{\sigma}[/tex]
Where [tex]x[/tex] is the score
[tex]\mu[/tex] is the mean
and [tex]\sigma[/tex] is the standard deviation
From the question,
[tex]x[/tex] = 121
[tex]\mu[/tex] = 100
[tex]\sigma[/tex] = 15
Then, the z score is
[tex]z =\frac{x - \mu}{\sigma}[/tex]
[tex]z =\frac{121 - 100}{15}[/tex]
[tex]z =\frac{21}{15}[/tex]
[tex]z =\frac{7}{5}[/tex]
z = 1.4
Hence, the z score is 1.4.
