Answer:
The z-score for this kernel is -2.3
Step-by-step explanation:
* Lets revise how to find the z-score
- The rule the z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
* Lets solve the problem
- The popping-times of the kernels in a certain brand of microwave
popcorn are normally distributed
- The mean is 150 seconds
- The standard deviation is 10 seconds
- The first kernel pops is 127 seconds
- We want to find the z-score for this kernel
∵ z-score = (x - μ)/σ
∵ x = 127
∵ μ = 150
∵ σ = 10
∴ z-score = (127 - 150)/10 = -23/10 = -2.3
* The z-score for this kernel is -2.3
Answer:
One hour’s sleep before midnight is worth three after.
Given is the number of science fiction books = 48
Let the number of mystery books be = x
Let the number of biographies be = y
Ratio of the number of mystery books to the number of science fiction books is 4:3 so
=

Ratio of the number of science fiction books to the number of biographies is 4:5 so 
=

Hence there are 48 science fiction books, 64 mystery books and 60 biographies.
So total number of books are = 