Answer:
2.5% of drivers have a reaction time more than 2.14 seconds
16% of drivers have a reaction time less than 1.78 seconds
84% of drivers have a reaction time less than 2.02 seconds
Step-by-step explanation:
The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
In this problem, we have that:
Mean = 1.9s
Standard deviation = 0.12
What percentage of drivers have a reaction time more than 2.14 seconds?
2.14 = 1.9 + 2*0.12
So 2.14 is two standard deviations above the mean.
Of the 50% of the measures above the mean, 95% are within 2 standard deviations of the mean, so, below 2.14. The other 5% is above.
0.05*0.5 = 0.025
2.5% of drivers have a reaction time more than 2.14 seconds
What percentage of drivers have a reaction time less than 1.78 seconds?
1.78 = 1.9 - 0.12
So 1.78 is one standard deviation below the mean.
Of the 50% of the measures that are below the mean, 68% are within one standard deviation of the mean, that is, greater than 1.78.
100 - 68 = 32
0.32*50 = 0.16
16% of drivers have a reaction time less than 1.78 seconds
What percentage of drivers have a reaction time less than 2.02 seconds?
2.02 = 1.9 + 0.12
So 2.02 is one standard deviation above the mean.
Of the measures that are below the mean, all are below 2.02.
Of those that are above, 68% are below 2.02.
0.5 + 0.68*0.5 = 0.84
84% of drivers have a reaction time less than 2.02 seconds
= 25.3