Application of the Normal Distribution and draw the curve

1. In a city, it is estimated that the maximum temperature in June is normally distributed with a mean of 28 and a standard deviation of 5.4. Calculate the number of days in this month in which it is expected to reach a maximum of between 22 and 31.

2.The mean weight of 800 college students is 56 kg and the standard deviation is 5 kg. Assuming that the weight is normally distributed, determine how many students weigh:

a. Between 60 kg and 70 kg.

b. More than 68 kg.

3. Several intelligence tests follow a normal distribution with a mean of 100 and a standard deviation of 15.

a. Determine the percentage of the population that would obtain a score between 95 and 110.

b. For a population of 2,500, how many are expected to have a score above 125?