Answer :
The Z-score is (b) -1.64.
Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.
To find the z-score corresponding to an observation of 4.7, we can use the formula:
z = (x - mu) / sigma
where x is the observation, mu is the mean, and sigma is the standard deviation.
Given that X-N(5.7, 0.61) we can substitute
z = (4.7 - 5.7) / 0.61 = -1.64
So the answer is (b) -1.64.
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Final answer:
To find the z-score of an observation of 4.7 in a distribution with a mean of 5.7 and a standard deviation of 0.61, the formula (X - μ) / σ is used, resulting in a z-score of -1.64.
Explanation:
The question asks for finding the z-score corresponding to an observation of 4.7 when the distribution has a mean (μ) of 5.7 and a standard deviation (σ) of 0.61. To find the z-score, we use the formula:
z = (X - μ) / σ
Plugging in the values gives us:
z = (4.7 - 5.7) / 0.61 = -1.64
Therefore, the z-score corresponding to an observation of 4.7 is -1.64, which means option b. -1.64 is the correct answer.
