Question

For a normally distributed population with a mean of 450 and standard deviation of 20 answer the following questions.

BLANK #1: What is the probability of finding a value below 411.2? (ANSWER IN DECIMAL FORM TO 4 DECIMAL PLACES)

BLANK #2: What percent of values are above 476.6? (ANSWER AS A PERCENT TO 2 DECIMAL PLACES...INCLUDE PERCENT SIGN WITH ANSWER)

BLANK #3: The bottom 20% of observations are below what value? (ANSWER TO 2 DECIMAL PLACES)

BLANK #4: What value would you expect to find the top 10% above? (ANSWER TO 2 DECIMAL PLACES)

Answer 1

Solution :

Given that ,

mean = = 450

standard deviation = = 20

BLANK #1:

P(x < 411.2) = P[(x - ) / < (411.2 - 450) /20 ]

= P(z < -1.94)

= 0.0262. ,

Probability = 0.0262

BLANK #2:

P(x > 476.6) = 1 - P(x < 476.6)

= 1 - P[(x - ) / < (476.6 450) /20 )

= 1 - P(z < 1.33)

= 1 - 0.9082

0.0918 = 9.18%

Percent = 9.18%

BLANK #3:

Using standard normal table ,

P(Z < z) = 20%

P(Z < z) = 0.2

P(Z < -0.84) = 0.2

z = -0.84

Using z-score formula,

x = z * +

x = -0.84 * 20 + 450 = 433.20

The bottom 20% of observations are below the value is 433.20

BLANK #4

Using standard normal table ,

P(Z > z) = 10%

1 - P(Z < z) = 0.1

P(Z < z) = 1 - 0.1 = 0.9

P(Z < 1.28) = 0.9

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 20 + 450 = 475.60

value the top 10% above is 475.60