Question

8. The mean of the winning scores of a bowling tournament over the last 10 years was 279, with a standard deviation of 3. Considering that the scores were in a normal
distribution, how many scores were below 282?

Answer 1

We Answer:

84.134% of the scores

Step-by-step explanation:

-This questions needs as to determine the probability of scores less than 282 then find the expectation;

-Let X be the score of a random selection:

$P(X<282)=P(z<\frac{ X-\mu}{\sigma})\\\\\\=P(z<\frac{282-279}{3})\\\\\\=P(z<1)\\\\=0.84134$

$=84.134\%$

The probability of scores below 282 is 0.84134 or 84.134%

Hence, 84.134% of the scores were below 282