Question

a researcher measured the writing speed of 300 right-handed and 100 left-handed people. the right-handed group had a mean of 100 and a standard deviation of 8 while the left-handed group had a mean of 84 and a standard deviation of 10. assume the distributions are normal. how many left-handed people wrote faster than the average right-handed person did?

Explanation:

Step1: Calculate z-score for left-handers

We need to find the z-score of the average right-handed speed (100) in the left-handed distribution. The z-score formula is $z=\frac{X-\mu}{\sigma}$, where $X=100$, $\mu=84$, $\sigma=10$.
$z=\frac{100-84}{10}=1.6$

Step2: Find upper tail probability

Look up $z=1.6$ in the standard normal table. The cumulative probability for $z=1.6$ is 0.9452. The probability of being faster (upper tail) is $1-0.9452=0.0548$.

Step3: Calculate number of left-handers

Multiply the probability by the total number of left-handers (100).
$\text{Number}=100\times0.0548=5.48$
Round to the nearest whole number since we count people.

Answer:

Approximately 5 left-handed people wrote faster than the average right-handed person.