Question

Use the 68-95-99.7 rule to solve the problem. Assume that a distribution has a mean of 21 and a standard deviation of 4. What percentage of the values in the distribution do we ex between 17 and 217 25% 34% 68% ОО 17% Question 35 of 40

Answer 1

A mean of '21' & a standard deviation of '4' is given for a normal distribution. We have to find the percentage of values in the distribution that lie between '17' & '21'.

To do so, we made use of Normal distribution diagram and found that

"34%" of values lie between 17 & 21. second optiomn

Given data- A distribution has a mean of '21 and a standard deviation of 4 M = 21 0 = 4 t we have to find the percentage of the values in the distribution lying between 17 and 21. tolue have to use "68-95-99.7" rule or Empirical rule to do so. to The Empirical or 68-95-99-7 rule states that: For a random variable y with a normal distribution with mean pe and standard deviation o - 687. of the Sy values lie within one standard deviation of the meanphi..., between lo and tio of the mean. - 95% of the sivalues lie within two standard deviations of the meam que se between 20 and +20 of the meam. - 99.7% of the s' values lie within three standard deviations of the mean it', e., between -30 and +30 of the mean. The above points can be clecully observed in the figure beside. This figure. 'is called the Normal distribution diagram. We are going to make use of this diagram to solve the given problem, M *In the given problem, mean, M=2) and Stemd curd deviation, 54. So, we 99.7% of reclues lie have values for the Normal distribution diagram as. 21+1(h)=25: M+2- =21+2(4)=29; 4436 =214314) 33 68% of values lie here Mean line 2 95% of values the here here - Mtlo