What is the theoretical probability of picking a

Use technology or a z-score table to answer the question.

Alik [6]

Answer:

The second choice: Approximately $65.2\%$ of the pretzel bags here will contain between 225 and 245 pretzels.

Step-by-step explanation:

This explanation uses a z-score table where each $z$ entry has two decimal places.

Let $\mu$ represent the mean of a normal distribution of variable $X$ . Let $\sigma$ be the standard deviation of the distribution. The z-score for the observation $x$ would be:

$\displaystyle z = \frac{x - \mu}{\sigma}$ .

In this question,

$\mu = 240$ .
$\sigma = 9.3$ .

Calculate the z-score for $x_1 = 225$ and $x_2 = 245$ . Keep in mind that each entry in the z-score table here has two decimal places. Hence, round the results below so that each contains at least two decimal places.

$\begin{aligned} z_1 &= \frac{x_1 - \mu}{\sigma} \\ &= \frac{225 - 240}{9.3} \approx -1.61\end{aligned}$ .

$\begin{aligned} z_2 &= \frac{x_2 - \mu}{\sigma} \\ &= \frac{245 - 240}{9.3} \approx 0.54\end{aligned}$ .

The question is asking for the probability $P(225 \le X \le 245)$ (where $X$ is between two values.) In this case, that's the same as $P(-1.61 \le Z \le 0.54)$ .

Keep in mind that the probabilities on many z-table correspond to probability of $P(Z \le z)$ (where $Z$ is no greater than one value.) Therefore, apply the identity $P(z_1 \le Z \le z_2) = P(Z \le z_2) - P(Z \le z_1)$ to rewrite $P(-1.61 \le Z \le 0.54)$ as the difference between two probabilities:

$P(-1.61 \le Z \le 0.54) = P(Z \le 0.54) - P(Z \le -1.61)$ .

Look up the z-table for $P(Z \le 0.54)$ and $P(Z \le -1.61)$ :

$P(Z \le 0.54)\approx 0.70540$ .
$P(Z \le -1.61) \approx 0.05370$ .

$\begin{aligned}& P(225 \le X \le 245) \\ &= P\left(\frac{225 - 240}{9.3} \le Z \le \frac{245 - 240}{9.3}\right)\\&\approx P(-1.61 \le Z \le 0.54) \\ &= P(Z \le 0.54) - P(Z \le -1.61)\\ &\approx 0.70540 - 0.05370 \\& \approx 0.65.2 \\ &= 65.2\% \end{aligned}$ .

3 0

4 years ago

Fine dy/dx if x/(x-y) =log[a/(x-y)

Genrish500 [490]

Answer:

<h2>hope it helps you see the attachment </h2>

5 0

3 years ago

Sching Equations with Variables on both sides 1 A Acelas Solve for x. X-6 = 5(x + 2)

Allisa [31]

Answer:

Step-by-step explanation:

here you go mate

step 1

x-6 = 5(x + 2) equation/Question

step 2

x-6 = 5(x + 2) simplify

x+(-)6=5x+10

x-6=5x+10

step 3

x-6=5x+10 subtract 5x

-4x-6=10

step 4

-4x-6=10 add 6

-4x=16

step 5

$\frac{-4x}{-4}=\frac{16}{-4} \\$

answer

x=-4

5 0

3 years ago

Sin^2(alpha) + cos^2(alpha)=? Fast plz sir is asking me rn lol

Crazy boy [7]

Answer:

the answer is 1

hope it helps

4 0

4 years ago

Suppose that the water level of a river is 34 feet and that it is receding at a rate of her foot per day right in equation and h

Ghella [55]

Answer: it will take 9 days

Step-by-step explanation:

The water level was initially at 34feet it was receding at the rate of a foot per day. The rate at which it was receding is linear, thus, it is in an arithmetic progression. The formula for the nth term of an arithmetic progression is expressed as

Tn = a+(n-1)d

Where

a is the first term if the sequence

d is the common difference

n is the number of terms.

From the information given,

a = 34 feet because it is the initial height

n is the number of days it will take to get to 26 ft

d = -1 because it is decreasing by 1 foot per day.

Tn = T26 = 26 feet. Therefore, the equation will be

Tn = 34 -1(n-1)

To find for T26,

26= 34 + (n - 1)-1

26 - 34 = -n + 1

n - 1 = 8

n = 8 + 1 = 9

8 0

3 years ago