Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 15. Using the empirical rule, what percentage of IQ scores are at least 59? Please do not round your answer.

Answer 1

Answer:

1.35%

Step-by-step explanation:

Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 15. Using the empirical rule, what ? Please do not round your answer.

Empirical rule formula states that:

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

We don't know the number of Standard deviation yet , hence:

Mean = 104

Standard deviation = 15.

At least 59

Hence:

104 - 15x = 59

104 - 59 = 15x

45 = 15x

x = 45/15

x = 3

Hence, At least 59 is 3 standard deviations away from the mean on one side of the distribution thus,

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

100% - 99.7%

= 0.003

Since it is on one side of the distribution:

= 1.5% - 0.3%

= 0.015 - 0.0015

= 0.00135

Converting to percentage

= 1.35%

The percentage of IQ scores that are at least 59 is 1.35%