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The figure above shows the standard normal distribution with mean 0 an
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01 Aug 2023, 08:36
01 Aug 2023, 08:36
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The figure above shows the standard normal distribution with mean 0 and standard deviation 1, including approximate percent of the distribution corresponding to the six regions shown above. The random variable x is normally distributed with standard deviation of 10 and value x = 135 is at the 20th percentile of the distribution. Of the following which is the best estimate of the mean of the distribution?
A. 140
B. 150
C. 160
D. 165
E. 170
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Re: The figure above shows the standard normal distribution with mean 0 an
[#permalink]
16 Sep 2023, 23:36
16 Sep 2023, 23:36
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Expert Reply
OE
If we consider normal distribution curve given in the question,
We know value at 20th percentile would lie in between ‘𝑀 – 𝐷’ and ‘𝑀’.
Where 𝑀 is mean and 𝐷 is standard deviation.
It is given that, value is at 20th percentile is 135
So, we can say ‘𝑀 – 𝐷’ < 𝑥 < 𝑀
𝑀 – 10 < 135 < 𝑀
𝑀 – 10 < 135 and 135 < 𝑀
𝑀 < 145 and 𝑀 > 135
135 < 𝑀 < 145
Out of the available answer choices, we can say that
𝑀 = 140
If we consider normal distribution curve given in the question,
We know value at 20th percentile would lie in between ‘𝑀 – 𝐷’ and ‘𝑀’.
Where 𝑀 is mean and 𝐷 is standard deviation.
It is given that, value is at 20th percentile is 135
So, we can say ‘𝑀 – 𝐷’ < 𝑥 < 𝑀
𝑀 – 10 < 135 < 𝑀
𝑀 – 10 < 135 and 135 < 𝑀
𝑀 < 145 and 𝑀 > 135
135 < 𝑀 < 145
Out of the available answer choices, we can say that
𝑀 = 140
gmatclubot
Re: The figure above shows the standard normal distribution with mean 0 an [#permalink]
16 Sep 2023, 23:36
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