Help asap! giving brainliest!
1 answer:
You might be interested in
Answer:
(b) The middle 68% of Jiffy Corn Muffin Mix boxes contain between <u>9.90 ounces</u> and <u>10.10 ounces</u> of corn muffin mix.
(c) The percentage of Jiffy Corn Muffin Mix boxes containing more than 10.3 ounces or less than 9.7 ounces of corn muffin mix is 16%.
(d) The percentage of iffy Corn Muffin Mix boxes containing more than 10.2 ounces of corn muffin mix is 2.3%.
(e) The percentage of Jiffy Corn Muffin Mix boxes containing less than 10.1 ounces of corn muffin mix is 84%.
Step-by-step explanation:
Let the random variable <em>X</em> be defined as the amount of corn muffin mix in a Jiffy Corn Muffin Mix box.
The random variable <em>X</em> follows a Normal distribution with mean, <em>μ</em> = 10.0 ounces and standard deviation, <em>σ</em> = 0.10 ounces.
(b)
According to the Empirical rule, 68% of the data from a Normal distribution lies within one standard deviation of mean.
That is:
P (x₁ < X < x₂) = 0.68
P (μ - σ < Z < μ + σ) = 0.68
Then,
P (10.0 - 0.10 < Z < 10.0 + 0.10) = 0.68
P (9.90 < Z < 10.10) = 0.68
Thus, the middle 68% of Jiffy Corn Muffin Mix boxes contain between <u>9.90 ounces</u> and <u>10.10 ounces</u> of corn muffin mix.
(c)
Compute the probability that Jiffy Corn Muffin Mix boxes contain more than 10.3 ounces or less than 9.7 ounces of corn muffin mix as follows:
P (X > 10.3 ∪ X < 9.7) = 1 - P (9.7 < X < 10.3)
Thus, the percentage of Jiffy Corn Muffin Mix boxes containing more than 10.3 ounces or less than 9.7 ounces of corn muffin mix is 16%.
(d)
Compute the probability of Jiffy Corn Muffin Mix boxes contain more than 10.2 ounces of corn muffin mix as follows:
Thus, the percentage of iffy Corn Muffin Mix boxes containing more than 10.2 ounces of corn muffin mix is 2.3%.
(e)
Compute the probability that a randomly selected Jiffy Corn Muffin Mix box contains less than 10.1 ounces of corn muffin mix as follows:
Thus, the percentage of Jiffy Corn Muffin Mix boxes containing less than 10.1 ounces of corn muffin mix is 84%.