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%
