Mathematics, 18.03.2021 01:20 loganrose50

Burger Queen a popular fast food restaurant among college students has undertaken a study to determine the weights of the hamburgers served in its new location in San Marcos, TX. Half pounders should weigh at least 8 ounces. The weight is assumed to be normally distributed. A sample of 500 hamburgers reveals the average precooked weight to be 8.02 ounces, with a standard deviation of .4 ounce. 1. What is the probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces?
2. What is the probability that a hamburger selected at random with less than 7.52 ounces?

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Answer from: emilycolley2

1. 0.2422 = 24.22% probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces

2. 0.1056 = 10.56% probability that a hamburger selected at random with less than 7.52 ounces.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

A sample of 500 hamburgers reveals the average precooked weight to be 8.02 ounces, with a standard deviation of .4 ounce.

This means that $\mu = 8.02, \sigma = 0.4$

1. What is the probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces?

This is the pvalue of Z when X = 8.02 subtracted by the pvalue of Z when X = 7.76. So

X = 8.02

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8.02 - 8.02}{0.4}$

Z = 0

Z = 0 has a pvalue of 0.5

X = 7.76

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{7.76 - 8.02}{0.4}$

Z = -0.65

Z = -0.65 has a pvalue of 0.2578

0.5 - 0.2578 = 0.2422

0.2422 = 24.22% probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces.

2. What is the probability that a hamburger selected at random with less than 7.52 ounces?

This is the pvalue of Z when X = 7.52. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{7.52 - 8.02}{0.4}$

Z = -1.25

Z = -1.25 has a pvalue of 0.1056

0.1056 = 10.56% probability that a hamburger selected at random with less than 7.52 ounces.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is