For a variable that is normally distributed with a mean of 50 and a standard deviation of 5, approximately _? of the scores are between _?. A)95%, 45 and 55 B)95%, 40 and 60 C)68%, 40 and 60 D)95%, 35 and 65 E)99%, 40 and 60

Question

For a variable that is normally distributed with a mean of 50 and a standard deviation of 5, approximately _? of the scores are between _?.  A)95%, 45 and 55  B)95%, 40 and 60  C)68%, 40 and 60  D)95%, 35 and 65  E)99%, 40 and 60

ottcomn · Accepted Answer

Step 1  Empirical rule:  For symmetric or normal distributions,  68% of values fall within one standard deviation from the mean. That is, (m – s, m + s).  95% of values fall within two standard deviations from the mean. That is, (m – 2*s, m + 2*s).  7% of values fall within three standard deviations from the mean. That is, (m – 3*s, m + 3*s).  Step 2  Calculations:  The random variable x follows normal distribution with mean 50 and standard deviation 5.  That is, m = 50 and s = 5.  The calculation based on empirical rule is given below:  One σ limits:  (μ±σ)=(5−−5,50+5)=(45,55)  68% of scores are between 45 and 55.  Two sigma limits:  (μ±2σ)=(50−2×5,50+2×5)=(40,60)  95% of scores are between 40 and 60.  Three σ limits:  (μ±3σ)=(50−3×5,50+3×5)=(35,65)  99% of scores are between 35 and 65.  Step 3  Obtain the correct option:  From the given 5 options, option (B) states that 95% of the scores lie between 40 and 60.  Hence, option (B) is correct.  Step 4  Answer:  Option (B) is correct.

For a variable that is normally distributed with a mean of 50 and a standard deviation of 5, approximately _? of the scores are between _?. A)95%, 45 and 55 B)95%, 40 and 60 C)68%, 40 and 60 D)95%, 35 and 65 E)99%, 40 and 60

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