Question

The observatory of a city studied the weather condition in winter. A series of weather data was recorded. (a) For each of the following data collected, state whether it is numerical or categorical variable and further indicate it is discrete, continuous, nominal or ordinal. (i) Number of days having severe snow. (ii) The intensity of snowfall (i.e. light, moderate, heavy). (iii) The lowest temperature (in∘C ) in each day. (b) Based on the past records, the probability of a day having severe snow is 0.06 . Given that a day having severe snow is independent to the other days. Find the probability that in a given week: (i) there will be 0 day with severe snow. (ii) there will be 3 or more days with severe snow.

Answer 1

In (a), the data type is stated for each item. In (b), the probabilities of 0 days and 3 or more days with severe snow in a given week are calculated.

Step-by-step explanation:

(a) For each of the following data collected:

1. (i) Number of days having severe snow: Numerical, Discrete
2. (ii) The intensity of snowfall (i.e. light, moderate, heavy): Categorical, Nominal
3. (iii) The lowest temperature (in∘C) in each day: Numerical, Continuous

(b) Based on the past records, the probability of a day having severe snow is 0.06. Given that a day having severe snow is independent to the other days, the probability that in a given week:

1. (i) there will be 0 day with severe snow: (0.94)^7 = 0.5184
2. (ii) there will be 3 or more days with severe snow: 1 - P(no days or 1 or 2 days with severe snow) = 1 - [(0.94)^7 + 7C1 * (0.06) * (0.94)^6 + 7C2 * (0.06)^2 * (0.94)^5] = 0.9633