91影视

The data for the misorientation angle (degrees) is provided.

The relative frequency table is given as,

a.

Let x represents the sampled angles.

The proportion of the sampled angles that are smaller than 15 degrees is computed as,

\(\begin{aligned}P\left( {x < 15} \right) &= P\left( {0 - 5} \right) + P\left( {5 - 10} \right) + P\left( {10 - 15} \right)\\ &= 0.177 + 0.166 + 0.175\\ &= 0.518\end{aligned}\)

Therefore, the percentage of the sampled angles that are smaller than 15 degrees is 51.8% which is more than 50%.

Yes, it is true that more than 50% of the sampled angles are smaller than 15掳, as asserted in the paper.

The data for the misorientation angle (degrees) is provided.

The relative frequency table is given as,

b.

Let x represents the sampled angles.

The proportion of the sampled angles that are atleast 30 degrees is computed as,

\(\begin{aligned}P\left( {x \ge 30} \right) &= P\left( {30 - 40} \right) + P\left( {40 - 60} \right) + P\left( {60 - 90} \right)\\ &= 0.078 + 0.044 + 0.030\\ &= 0.152\end{aligned}\)

Therefore, the percentage of the sampled angles that are at least 30 degrees is 0.152.