Each of the following curves fails to be a normal curve. Give reasons why these

Question

Each of the following curves fails to be a normal curve. Give reasons why these curves are not normal curves. 2. Accordin to the empiried rule, for a distribution that is symmetrical and bell-shaped, approximately of the data values will lie within three standard deviations on each side of the mean. 3. Assuming that the heights of boys in high school basket- ball tournment are normally distributed, with mean 70 inches and standard deviation 2.5 inches, how many boys in a group of 40 do we expect to be taller than 75 inches? 4. Let x be random variable that represents the length of time it takes a student to complete Dr. Gill's chemistry lab project. From long experience, it is Known that x has a normal distribution with mean mu = 3.6 hours and standard deviation sigmma = 0.5 hour.

Explanation / Answer

1a. The given graph is not a normal curve since it has two peaks. It is a bi-modal curve. A normal curve will have only one peak.

1b. A normal curve will not take negative values. But the graph in the given picture dips below x-axis hence it is not a normal curve.

2. Approximately 99.970 of data values will lie within the three standard deviations on each side of the mean. This is calculated as follows:

± = 68%

± 2 = 95%

± 3 = 99.79%ts

3. There will be one boy who will be taller than 75 inches. This is calcualted as follows:

We have to chart this out in a graph for better understanding:

Value of 75% = 2 + 0.590$ =2.59% = 0.025

0.025 (40) = 1

4. To convert standard x iterval to z Interval = 3.6 ; = 0.5%

1. x>=4.5

z = (4.5-3.6) / 0.5 = 1.8

= Z>=1.8

2. 3<= x <= 4

z = (3-3.6)/0.5 = -1.2 ;

z = (4 - 3.6) / 0.5 = 0.8

-1.2 <= z <= 0.8

3. x<= 2.5

z = (2.5 - 3.6) / 0.5 = -2.2

z<= -2.2

4. z <= -1 = -1(0.5)+3.6 = 3.1

--> x<= 3.1

5. 1 <= z <= 2

x = 1(0.5) + 3.6 = 4.1

x = 2(0.5) + 3.6 = 4.6

--> 4.1 <= x <= 4.6

6. Z >= 1.5

x = 1.5 (0.5) + 3.6 = 4.35

x >= 4.35

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