The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. What is the probability of a weight between 415 pounds and the mean of 400 pounds

The probability is

Step-by-step explanation:

From the question we are told that

   The population mean is  

   The  standard deviation is  

   The considered values are  

Given that the weight follows a normal distribution

     i.e      

Now the probability of a weight between 415 pounds and the mean of 400 pounds is mathematically as

So   is equal to Z (the standardized value of  X  )

Hence we have  

substituting values

From the standardized normal distribution table   and

So

NOTE :  This above  values obtained from the standardized normal distribution table can also be obtained using the P(Z) calculator at  (calculator dot net).

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

40% off the regular price is the correct answer.

step-by-step explanation: