Please complete in MATLAB Macrolepiota Procera The size of m

Please complete in MATLAB.

Macrolepiota Procera. The size of mushroom caps varies. While many species of Marasmius and Collybia are only 12 to 20 mm (1 /2 to 3/4 in.) in diameter, some fungi are nearly 200 mm (8 in.) across. The cap diameter of parasol mushroom (Macrolepiota procera, Fig. 6.19) is a normal random variable with parameters p - 230 mm and cr = 25 mm. Fig. 6.19 Parasol mushroom Macrolepiota procera. What proportion of parasol caps has a diameter between 200 and 250 mm? Five percent of parasol caps are larger than *o in diameter. Find xq.

Solution

a)

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    200      
x2 = upper bound =    250      
u = mean =    230      
          
s = standard deviation =    25      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.2      
z2 = upper z score = (x2 - u) / s =    0.8      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.11506967      
P(z < z2) =    0.788144601      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.673074931   [answer]

b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.95      
          
Then, using table or technology,          
          
z =    1.644853627      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    230      
z = the critical z score =    1.644853627      
s = standard deviation =    25      
          
Then          
          
x = critical value =    271.1213407   [answer]