Respuesta :
Answer: x= 3.5 is -2. The mean is 6.5.
z score to the left is 2
Step-by-step explanation:
X is a normally distributed random variable with μ=6.5 (mean) and σ=1.5 (standard deviation). To calculate the z-score,
z=x−μσ=3.5−6.51.5=−31.5=−2
This means that x=3.5 is two standard deviations (2σ) below or to the left of the mean. This makes sense because the standard deviation is 1.5. So, two standard deviations would be (2)(1.5)=3, which is the distance between the mean (μ=6.5) and the value of x (3.5).
Using the normal distribution, it is found that x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.
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In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is from the mean, above or below.
- X∼N(6.5,1.5), which means that [tex]\mu = 6.5, \sigma = 1.5[/tex].
- The measure is [tex]X = 3.5[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.5 - 6.5}{1.5}[/tex]
[tex]Z = -2[/tex]
The measure x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.
A similar problem is given at https://brainly.com/question/13383035
