The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1400 and the standard deviation is $145.

Question

965 1110 1255 1400 1545 1690 1835

What is the approximate percentage of buyers who paid between $965 and $1400?

%

What is the approximate percentage of buyers who paid between $1110 and $1400?

%

What is the approximate percentage of buyers who paid between $1255 and $1545?

%

What is the approximate percentage of buyers who paid less than $965?

%

What is the approximate percentage of buyers who paid more than $1690?

%

What is the approximate percentage of buyers who paid between $1400 and $1545?

%

Answer 1

The mean of the Normal Distribution (ND) for this problem, mu=$1400, and standard deviation is $145.

a). Since data follows a ND, we will get the z score corresponding the given value(s), and then get the percentage from the z table.

to get the percentage of buyers between 965 and 1400 (which is equal to mu),

z=(x-mu)/sigma= (965-1400)/145= -3.

the percentage from the z table is 0.4987. So approximately 49.87% buyers.

Alternatively, TI84 can be used to get the answer.

Use normcdf to get the percentages.

Lower=965, Upper=1400, mu=1400, sigma(standard dev.)=145. Compute to get the above answer.

b.)

percentage of buyers who paid between 1100 and 1400.

it is the same as above, either use Z csore and get the percentage from the z table or using graphing calculator,

lower=1100, upper=1400, mu=1400, sigma=145. Compute to get the answer=0.4807

c.)Normcdf

lower=1255, upper=1545, mean mu and sigma is the same.

Compute to get the answer=0.6827.

Alternatively, z scores can be calculated for each of the above two values, et percentages from the z table and subtract the two to get the the area in between.

d).

For less than 965,

use normcdf,

Lower will be a very small negative value as it is the entire area to the left of 965,

so lower=1E-99,upper=965, mu and sigma stay the same.

Compute to get the answer=0.0013

e).

Normcdf

to get the percentage of buyers who paid more than 1690, we need to get the entire tail area to the right of 1690.

hence, lower=1690, upper=a very large positive value 1E+99, mu and sigma are the same as before.

Compute to get the answer=0.0228

f).

Normcdf

lower=1400, upper=1545, mu and sigma stay the same. Compute to get the answer=0.3413.