Question

Mean=5.581 standard deviation= 1.114

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

1.)

Answer: The IQR values are 4.83 to 6.33.

Explanation:

For normally distributed data values,

Interquartile Range = Quartile 1 to Quartile 3

Quartile 1 = 25th percentile value

Quartile 3 = 75th percentile value

25th percentile

The 25th percentile value is obtained by calculating the z score,

The z score is obtained from the standard normal distribution table for probability = 0.15

75th percentile

The 75th percentile value is obtained by calculating the z score,

The z score is obtained from the standard normal distribution table for probability = 0.75

2.)

Answer:  IQR = 1.50

Explanation:

3.)

Answer: The 15th percentile is 4.43

Explanation:

The 15th percentile value is obtained by calculating the z score,

The z score is obtained from the standard normal distribution table for probability = 0.15

4.)

Answer: The 85th percentile is 6.73

Explanation:

The 85th percentile value is obtained by calculating the z score,

The z score is obtained from the standard normal distribution table for probability = 0.85

5.)

Answer: For a normally distributed data values,15% of data values lie below the 15the percentile value and 85% of data values lie below the 85th percentile value

6.)

Answer: Probability = 0.20

Explanation:

The probability is obtained by calculating the z score,

The probability is obtained from the z distribution table,