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Answer :
According to the statement the z-score corresponding to an observation of 4.7 is -1.64.
The z-score corresponds to the number of standard deviations an observation is away from the mean in a normal distribution.
To find the z-score for an observation of 4.7 in the given normal distribution X ~ N(5.7, 0.61), we can use the formula:
z = (observation - mean) / standard deviation
In this case, the mean (μ) is 5.7 and the standard deviation (σ) is 0.61.
Plugging in the values, we have:
z = (4.7 - 5.7) / 0.61
Calculating this, we get:
z = -1.64
Therefore, the z-score corresponding to an observation of 4.7 is -1.64.
To summarize, the correct answer is b) -1.64.
The z-score is a negative value because the observation is below the mean.
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