Question

Preview File Edit View Go Tools Window Help Ch6 normal distribution_Jab.pdt (page 1 of 2)-Edited Ch8 normal,distribution Jab.pdf (page 1 of 2) The Normal Distribution: Normal Distribution Lab Collect the Data: Measure the length of your pinkie finger (in cm.) Record the lengths of the entire class below. Round to the nearest 0.5 cm 2.5 5.5 6.5 6.5 6.5 6.5 6.5 6.5 2.5 5.5 5.5 5.5 7.5 4.5 6.5 6.5 6.5 6.5 Construct a histogram. Make S -6 nteralk sketch the ereaph using a ruler and pencil Scale the axes Frequency Length of Finger Draw a smooth curve through the top of the bars of the histogram. Use 1- 2 complete sentences to describe the general shape of the curve. (Keep it simple. Does the graph go straight across, does it have a V shape, does it have a hump in the middle or at either end, etc.?)

Answer 1

sol:

We classify the data in the following intervals.

IntervalFreq 2.5-3.5 3.5-4.5 4.5-5.5 5.5-6.5 6.5-7.5 Total 2 2 21 19 47

Histogram 21 19 3 2.5-3.5 3.5-4.5 4.5-5.5 5.5-6.5 6.5-7.5

The distribution seems to be negatively skewed as the tail is longer on the left.

From the given Data:

Q₁ (1^st Quartile) = 5.5

Q₃ (3^rd Quartile) = 6.5

IQR goes from Q₁ to Q₃ ie 5.5 to 6.5

IQR = Q_{3 ­­­}– Q₁ = 6.5 – 5.5 = 1

15^th Percentile = 5.45

85^th Percentile = 7

Median = 6

Mean = 5.94

Std Dev = 1.06

n = 47

Std Error = 1.06/47^1/2 = 0.15

So,

P(X>6.5) = 1- P(X<6.5) = 1 – P{z< (6.5-5.94)/0.15} = 1 – P(Z<3.66) ~ 0

85^th percentile means that the score is greater than 85% of the population’s pinkie finger length.

PS: 'Analyse the data' Dataset is missing.