need stats homework completed showing work

1)     In China, 4-year-olds average 3 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly survey one Chinese 4-year-old living in a rural area. We are interested in the amount of time the child spends alone per day      

a)     Suppose this child spends 4.25 hours a day unsupervised. How far away from the mean is this (in terms of standard deviations).

 

 

 

 

 

 

 

 

b)     What is the probability that a child spends more than 4.25 hours a day unsupervised? (use your Z table )

 

 

 

 

 

 

 

 

 

 

c)     Suppose you pick another random Chinese child and find he spends 1 hour a day unsupervised. How far away from the mean is this (in terms of standard deviations).

 

 

 

 

 

 

 

 

 

d)     What is the probability that a child spends less than 1 hour a day unsupervised? (use your Z table)

 

 

 

2)     Now let’s say that in China the population has a mean age of 16 with a standard deviation of 4.5. What is the probability of selecting an individual at random between the ages of 21 and 25?

 

 

 

 

 

 

 

 

 

3)     The boss must distribute salary raises to her employees.  She has decided that the mean raise will be $2000 with a standard deviation of $400 and that the distribution will be normal and based on productivity.

           

a) The most productive 5.05% of employees will receive a raise that is greater than or equal to $________ each

 

 

 

 

 

 

 

 

 

 

b) The least productive 10.2% of employees will receive a raise that is less than or equal to $________ each