Assume that the amount of time, in hours, that college students spend per week on homework is normally distributed with a mean of 15 hours and a standard deviation of 3 hours. If 75 students are selected at random, what is the probability that they average: more than 14 hours per week on homework between 14 and 16 hours per week on homework less than 15.5 hours of homework per week Answer in complete sentences. Be sure to include all relevant calculations.

Yoonie is a personnel manager in a large corporation. Each month she must review  10  of the employees. From past experience, she has found that the reviews take her approximately  4  hours each to do with a population standard deviation of  1.1  hours. Let  X  be the random variable representing the time it takes her to complete one review. Assume  X  is normally distributed. Let  X¯¯¯  be the random variable representing the mean time to complete the  10  reviews. Assume that the  10  reviews represent a random set of reviews. (a) What is the mean, standard deviation, and sample size? Mean = Standard Deviation = Sample Size = (b) Complete the distributions. Round all decimals to four decimal places. X∼ ( Number, Number)   X¯¯¯∼ ( Number, Number)

Assume that the square footage of a residential house in the US is normally distributed with a mean=1000 and standard deviation=150 square feet. If we select a random house what is the probability that it will be at most 1050 square feet?

The 3-point shooter star of your favourite team usually attempts twelve 3-point shots in a basketball game. The team record shows that the shooter makes 45% of all 3-point shots attempted in a game. Assuming that the shots are independent of each other,what is probability that the star will make shots at least 2 standard deviation more than the expected?