Eruptions of the Old Faithful geyser in Yellowstone National Park typically last from 1.5 to 5 minutes. Between eruptions are dormant periods, which typically last from 50 to 100 minutes. A dormant period can also be thought of as the waiting time between eruptions. The durations in minutes for 60 consecutive dormant periods are given in the following table. It is desired to predict the length of a dormant period from the length of the dormant period immediately preceding it. To express this in symbols, denote the sequence of dormant period $T_{1}, \ldots, T_{60}.$ It is desired to predict $T_{i+1}$ from $T_i.$

$$\begin{matrix} \text{i} & T_i & \text{i} & T_i & \text{i} & T_i & \text{i} & T_i & \text{i} & T_i & \text{i} & T_i\\ \text{1} & \text{80} & \text{11} & \text{56} & \text{21} & \text{82} & \text{31} & \text{88} & \text{41} & \text{72} & \text{51} & \text{67}\\ \text{2} & \text{84} & \text{12} & \text{80} & \text{22} & \text{51} & \text{32} & \text{51} & \text{42} & \text{75} & \text{52} & \text{81}\\ \text{3} & \text{50} & \text{13} & \text{69} & \text{23} & \text{76} & \text{33} & \text{80} & \text{43} & \text{75} & \text{53} & \text{76}\\ \text{4} & \text{93} & \text{14} & \text{57} & \text{24} & \text{82} & \text{34} & \text{49} & \text{44} & \text{66} & \text{54} & \text{83}\\ \text{5} & \text{55} & \text{15} & \text{90} & \text{25} & \text{84} & \text{35} & \text{82} & \text{45} & \text{84} & \text{55} & \text{76}\\ \text{6} & \text{76} & \text{16} & \text{42} & \text{26} & \text{53} & \text{36} & \text{75} & \text{46} & \text{70} & \text{56} & \text{55}\\ \text{7} & \text{58} & \text{17} & \text{91} & \text{27} & \text{86} & \text{37} & \text{73} & \text{47} & \text{79} & \text{57} & \text{73}\\ \text{8} & \text{74} & \text{18} & \text{51} & \text{28} & \text{51} & \text{38} & \text{67} & \text{48} & \text{60} & \text{58} & \text{56}\\ \text{9} & \text{75} & \text{19} & \text{79} & \text{29} & \text{85} & \text{39} & \text{68} & \text{49} & \text{86} & \text{59} & \text{83}\\ \text{10} & \text{80} & \text{20} & \text{53} & \text{30} & \text{45} & \text{40} & \text{86} & \text{50} & \text{71} & \text{60} & \text{57}\\ \end{matrix}$$

a. Construct a scatterplot of the points $\left(T_{i}, T_{i+1}\right), \text { for } i=1, \ldots, 59.$ b. Compute the least-squares line for predicting $T_{i+1} \text { from } T_{I}.$ c. Find a 95% confidence interval for the slope $\beta_1.$ d. If the waiting time before the last eruption was 70 minutes, what is the predicted waiting time before the next eruption? e. Find a 98% confidence interval for the mean waiting time before the next eruption when the time before the last eruption was 70 minutes. f. Find a 99% prediction interval for the waiting time before the next eruption, if the time before the last eruption was 70 minutes.

a. ¿De cuántas formas su pueden sentar 3 niños y 3 niñas en una fila?

b. ¿De cuántas formas se pueden sentar 3 niños y 3 niñas en una fila, si los niños y niñas se deben sentar juntos cada uno?

c. ¿De cuántas formas si sólo los niños se deben sentar juntos?

d. ¿De cuántas formas si ningún par de personas del mismo sexo se pueden sentar juntos?

How do monocular and binocular depth cues differ?