Question

Question 3 2/3 pts A sample data set with a bell-shaped distribution and size n - 128 has mean -2 and standard deviation s- 1.1. Find the approximate number of observations in the data set that lie: 1. below -0.2; 3 2. below 3.1: 108 3. between -1.3 and 0.9. 19 (Round to the closest integer) Answer 1:

Answer 1

Here we have

$\mu$= 2.0, $\sigma$=1.1, n = 128

a) From normal distribution:-

$z = \frac{x-\mu }{\sigma }$

Z=(-.2-2)/1.1

z = - 2

P(z < - 2) = 0.0228

So the number of observations in the data set that lie below - 0.2 = 0.0228 × 128 = 2.91

The approximate number of observations in the data set that lie below - 0.2 = 3

b) Using normal distribution:-

$z = \frac{x-\mu }{\sigma }$

Z=(3.1-2)/1.1

z = 1

P(z < 1) = 0.8413

So the number of observations in the data set that lie below 3.1 = 0.8413 × 128 = 107.69

The approximate number of observations in the data set that lie below 3.1 = 108

c) Here

x₁ = - 1.3

x₂ = 0.9

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

z=(-1.3-2)/1.1 = - 3

z=(0.9-2)/1.1 = - 1

P(- 3< z < - 1) =P(z > - 1)-P(Z<-3)=.1587-.0013=.1574

So the number of observations in the data set that lie between - 1.3 and 0.9 = 128 × 0.1574 = 20.1472

The approximate number of observations in the data set that lie between - 1.3 and 0.9 = 20

Dear student your last part answer seems wrong.