91影视

First serve speed, x = 120 mph

Mean speed, 渭 = 112 mph

Standard deviation, 蟽 = 5 mph

The formula used:$z=\frac{x鈭�渭}{蟽}$

Calculate the $z鈭�$score,

$z=\frac{120鈭�112}{5}=\frac{3鈭�5.3}{0.9}=1.60$

To find the equivalent probability, use the normal probability table in the appendix.

The usual normal probability table for $P(z<1.60)$has a row that starts with $1.6$and a column that starts with$.00$

$$\begin{gathered} P(x<120)=P(z>1.60)=1鈭�P(z<1.60) \\ =1鈭�0.9452 \\ =0.0548 \\ =5.48\% \end{gathered}$$

Therefore,

Around $5.48\%$that time Djokovic hits his first serve faster than $120$mph.

Calculate the z 鈭� score,

$z=\frac{x鈭�渭}{蟽}=\frac{100鈭�112}{5}=鈭�2.40$

To find the equivalent probability, use the normal probability table in the appendix. See the standard normal probability table for $P(z<鈭�2.40)$and the row that starts with $-2.4$and the column that starts with$.00$

$$\begin{gathered} P(x<100)=P(z<鈭�2.40) \\ =0.0082 \\ =0.82\% \end{gathered}$$

Therefore,

Around $0.82\%$ of the first serves are slower than $100$ mph.

Calculate the $z鈭�$score,

$z=\frac{x鈭�渭}{蟽}=\frac{100鈭�112}{5}=鈭�2.40$

Or

$z=\frac{x鈭�渭}{蟽}=\frac{110鈭�112}{5}=鈭�2.40$

To find the equivalent probability, use the normal probability table in the appendix.

See the standard normal probability table for $P(z<鈭�2.40)$ and look for the row with $-2.4$ and the column with$.00$

Or

The usual normal probability table for $P(z<鈭�0.40)$has a row that starts with$-0.4$and a column that starts with$.00$

$$\begin{gathered} P(100<x<110)=P(鈭�2.40<z<鈭�0.40) \\ =P(z<鈭�0.40)鈭�P(z<鈭�2.40) \\ =0.3446鈭�0.0082 \\ =0.3364 \end{gathered}$$

Therefore,

Around $0.3364$of Djokovic鈥檚 first serves have speeds between $100$and $110$mph.