Question

Use the mean and standard deviation from your data and treat your sample as if it is a completely
symmetrical normal distribution, representative of the population at large, to answer the following.

Mean=6.1767

standard deviation.79696

Use 2 decimal places in this part and show all work leading to your answer.
1.) The IQR values are ___ to ___
2.) IQR = __.
3.)The 15th percentile is __.
4.)The 85th percentile is __.
5.)Using complete sentences, and on your own paper, explain the meaning of the 15th and the 85th
percentile of this distribution.
6.)The theoretical probability that a randomly chosen length is more than 6.5 cm =

Answer 1

Mean=6.1767

SD = 0.79696

From normal probability calculator, we have the following for the above normal distribution :

Q1 =5.639

Q3 = 6.714

The IQR value is 5.639 to 6.714

IQR = Q3-Q1 = 6.714 - 5.639 = 1.075.

15th percentile =5.351 ( from Normal Probability calculator )

85th percentile = 7.003 ( from Normal Probability calculator)

15th percentile means the point below which 15% of the total observations lie. Similarly, this is the same for the 85th percentile.

P( X > 6.5) = P[((X -6.1767) /0.79696)> 0.4057] = 1 - P(Z< = 0.4057) = 1-0.6575= 0.3425