Answer :
The z-score corresponding to an observation of 4.7 in a normal distribution with mean 5.7 and standard deviation 0.61 is -1.64.
To find the z-score, we use the formula:
z = (x - μ) / σ
Where:
x = observation (4.7 in this case)
μ = mean of the distribution (5.7 in this case)
σ = standard deviation of the distribution (0.61 in this case)
Substituting the given values into the formula, we get:
z = (4.7 - 5.7) / 0.61
= -1 / 0.61
≈ -1.64
Therefore, the z-score corresponding to an observation of 4.7 is approximately -1.64. This indicates that the observation is 1.64 standard deviations below the mean.
The z-score is a measure of how many standard deviations an observation is from the mean of a distribution. A positive z-score indicates that the observation is above the mean, while a negative z-score indicates that the observation is below the mean.
In this case, the z-score of -1.64 suggests that the observation of 4.7 is below the mean of 5.7. By using z-scores, we can standardize observations and compare them across different distributions or calculate probabilities associated with specific values.
Learn more about z-score here:
brainly.com/question/31871890
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