. Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito. (a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points) (b) 20% of Chipotle burritos weigh more than what weig

Complete Question

Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito.

(a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points)

(b) 20% of Chipotle burritos weigh more than what weight

a

b

Step-by-step explanation:

From question we are told that

     The population mean is

      The variance is

      The  consider weight is  

The  standard deviation is mathematically represented as

substituting values

Given that weight of Chipotle burritos follows a normal distribution the  the probability that a Chipotle burrito weighs less than x grams is mathematically represented as

Where   is  equal to z (the standardized values of the random number X )

So

substituting values

Now from the normal distribution table  the value for  is  

=>  

Let the  probability  of the Chipotle burritos weighting more that k be 20% so  

=>    

=>    

From the normal distribution table the value of z  for   is  

=>  

=>  

x = 138

Step-by-step explanation:

The 2 arcs above the diameter form a semicircle = 180°

x + 42 = 180 ( subtract 42 from both sides )

x = 138