Josh's throwing follows a normal distribution curve according to the question. Therefore, we can say that the probability of his throws reaching certain distances is represented by the normal distribution.
The normal distribution is sketched below:
From the distribution curve shown above, his mean throw distance is at the center and has the largest percentage of occurrence because his throws are usually around that distance.
When we examine the curve even further, we shall see that after the first standard deviation
(σ), the range of values his throws can take increases. This time his throws can be around any value greater than: MEAN + σ.
But the question asks us for the percentage of his throw distances that are within 2 standard deviations. Thus, they are asking for the area of the whole curve EXCEPT the two shaded regions at the tails of the curve shown above.
The normal distribution percentages for each standard deviation is given below:
From the distribution above, we can see that his throws can either be lower than his mean or
greater than his mean.
Therefore, we can add the percentages together:
13.5% + 34% + 34% + 13.5% = 95%
Therefore the final answer is 95%