Page 3 7 the local area and assume that X follows the Unifor

Page 3 7 the local area, and assume that X follows the Uniform distribution in the intervat em 3. (15 points) A weather forecaster predicts that the May rainfall in a local area will bs oayrain inches but has no idea where within the interval the amount will be. Let X be the am nfall in a local area will be between 4 ill be. Let X be the amount of May rain in 4 to 7 inches. a) What is the mean amount of rainfall in May? (5 pts) b) What is the standard deviation amount of rainfall in May? (5 pts) c) What is the probability that May rainfall will be less than 5.5 inches? (5 pts) Problem 4. (10 points) The amount of ore (in tons) in a segment of a mine is assumed to follow a normal distribution with mean 180 and standard deviation 40. Find the probability that the amount of ore is betwe 172 and 190 tons.

Solution

a)

Note that here,          
          
a = lower fence of the distribution =    4      
b = upper fence of the distribution =    7      

Thus, the mean, variance, and standard deviations are          
          
u = mean = (b + a)/2 =    5.5   [ANSWER]

*****************************

b)
  
s^2 = variance = (b -a)^2 / 12 =    0.75      

s = standard deviation = sqrt(s^2) =    0.866025404 [ANSWER]

*****************************

c)      

Note that P(x<c) = P(a<x<c) = (c-a)/(b-a). Thus, as          
          
c = critical value =    5.5      
          
Then          
          
P(x<c) =    0.5   [ANSWER]  
          

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!