Step-by-step explanation:
All steps are in pic above.
<u>N</u><u>o</u><u>t</u><u>e</u><u>:</u><u>i</u><u>f</u><u> </u><u>y</u><u>o</u><u>u</u><u> </u><u>h</u><u>a</u><u>v</u><u>e</u><u> </u><u>a</u><u>n</u><u>y</u><u> </u><u>questions</u><u> </u><u>a</u><u>b</u><u>o</u><u>u</u><u>t</u><u> </u><u>i</u><u>t</u><u> </u><u>l</u><u>e</u><u>t</u><u> </u><u>m</u><u>e</u><u> </u><u>k</u><u>n</u><u>o</u><u>w</u><u>.</u>
Using the normal distribution, it is found that 0.26% of the items will either weigh less than 87 grams or more than 93 grams.
In a <em>normal distribution</em> with mean
and standard deviation
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
- The mean is of 90 grams, hence
.
- The standard deviation is of 1 gram, hence
.
We want to find the probability of an item <u>differing more than 3 grams from the mean</u>, hence:



The probability is P(|Z| > 3), which is 2 multiplied by the p-value of Z = -3.
- Looking at the z-table, Z = -3 has a p-value of 0.0013.
2 x 0.0013 = 0.0026
0.0026 x 100% = 0.26%
0.26% of the items will either weigh less than 87 grams or more than 93 grams.
For more on the normal distribution, you can check brainly.com/question/24663213
Option B:
is the correct answer.
Explanation:
The exponential equation is 
If
, then 
Thus, the equation becomes

Applying log rule,
and thus the equation becomes

Since, we know that,
, using this we get,

Hence, the logarithmic equation which is equivalent to the exponential equation
is 
Thus, Option B is the correct answer.
Answer:
2+i times the square root of 7