Question

The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1000 and the standard deviation is $145.

What is the approximate percentage of buyers who paid between $1000 and $1290? 47.5 Correct%

What is the approximate percentage of buyers who paid between $1000 and $1145? 34 Correct%

What is the approximate percentage of buyers who paid less than $565? -.335 Incorrect%

What is the approximate percentage of buyers who paid less than $710? -2.685 Incorrect%

What is the approximate percentage of buyers who paid between $1000 and $1435? 49.85 Correct%

What is the approximate percentage of buyers who paid between $855 and $1145? 68 Correct%

Answer 1

SOLUTION:

From given data,

The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1000 and the standard deviation is $145.

Where,

Mean = = 1000

Standard deviation = = 145

Z = (X - ) / = (X - 1000) / 145

What is the approximate percentage of buyers who paid between $1000 and $1290? 47.5 Correct%

P(1000 < X < 1290) = P((1000 - 1000) / 145 < (X - ) / < (1290 - 1000) / 145​​​​​​​)

P(1000 < X < 1290) = P(0 / 145​​​​​​​ < Z < 290 / 145​​​​​​​)

P(1000 < X < 1290) = P(0 < Z < 2)

P(1000 < X < 1290) = P(Z < 2)-P(Z < 0)

P(1000 < X < 1290) = 0.97725-0.50000

P(1000 < X < 1290) = 0.47725

P(1000 < X < 1290) = 47.7 %

What is the approximate percentage of buyers who paid between $1000 and $1145? 34 Correct%

P(1000 < X < 1145) = P((1000 - 1000) / 145​​​​​​​ < (X - ) / < (1145 - 1000) / 145​​​​​​​)

P(1000 < X < 1145) = P(0 / 145​​​​​​​ < Z < 145 / 145​​​​​​​)

P(1000 < X < 1145) = P(0 < Z < 1)

P(1000 < X < 1145) = P(Z < 1)-P(Z < 0)

P(1000 < X < 1145) = 0.84134-0.50000

P(1000 < X < 1145) = 0.34134

P(1000 < X < 1145) = 34.1 %

What is the approximate percentage of buyers who paid less than $565? -.335 Incorrect%

P(X < 565) = P((X - ) / < (565 - 1000) / 145​​​​​​​ )

P(X < 565) = P(Z < (565 - 1000) / 145​​​​​​​ )

P(X < 565) = P(Z < -435/ 145​​​​​​​ )

P(X < 565) = P(Z < - 3)

P(X < 565) = 0.00135

P(X < 565) = 0.13 %

What is the approximate percentage of buyers who paid less than $710? -2.685 Incorrect%

P(X < 710) = P((X - ) / < (710 - 1000) / 145​​​​​​​ )

P(X < 710) = P(Z < (710 - 1000) / 145​​​​​​​ )

P(X < 710) = P(Z < -290/ 145​​​​​​​ )

P(X < 710) = P(Z < - 2)

P(X < 710) = 0.02275

P(X < 710) = 2.27 %

What is the approximate percentage of buyers who paid between $1000 and $1435? 49.85 Correct%

P(1000 < X < 1435) = P((1000 - 1000) / 145​​​​​​​ < (X - ) / < (1435 - 1000) / 145​​​​​​​)

P(1000 < X < 1435) = P(0 / 145​​​​​​​ < Z < 435 / 145​​​​​​​)

P(1000 < X < 1435) = P(0 < Z < 3)

P(1000 < X < 1435) = P(Z < 3)-P(Z < 0)

P(1000 < X < 1435) = 0.99865-0.50000

P(1000 < X < 1435) = 0.49865

P(1000 < X < 1435) = 49.8 %

What is the approximate percentage of buyers who paid between $855 and $1145? 68 Correct%

P(855 < X < 1145) = P((855 - 1000) / 145​​​​​​​ < (X - ) / < (1145 - 1000) / 145​​​​​​​)

P(855 < X < 1145) = P(-145 / 145​​​​​​​ < Z < 145 / 145​​​​​​​)

P(855 < X < 1145) = P(-1 < Z < 1)

P(855 < X < 1145) = P(Z < 1)-P(Z < -1)

P(855 < X < 1145) = 0.84134-0.15866

P(855 < X < 1145) = 0.68268

P(855 < X < 1145) = 68.3 %