MATHEMATICS COLLEGE

The amount of cream sauce on the fettuccine at Al Fred-O's follows a Normal distribution, with a mean of 3.78 ounces and a standard deviation of 0.14 ounce. A random sample of 12 plates of fettuccine is selected every day and the sauce is measured. What is the probability that the mean weight will exceed 3.81 ounces

Answers

Answer 1

Answer:

Answer:

22.66% probability that the mean weight will exceed 3.81 ounces

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples 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:

$Z = (X - \mu)/(\sigma)$

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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$

In this problem, we have that:

$\mu = 3.78, \sigma = 0.14, n = 12, s = (0.14)/(√(12)) = 0.04$

What is the probability that the mean weight will exceed 3.81 ounces

This probability is 1 subtracted by the pvalue of Z when X = 3.81. So

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (3.81 - 3.78)/(0.04)$

$Z = 0.75$

$Z = 0.75$ has a pvalue of 0.7734

1 - 0.7734 = 0.2266

22.66% probability that the mean weight will exceed 3.81 ounces

Answer 2

Answer:

Answer:

Correct answer is 0.2290

Step-by-step explanation:

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B. The difference between the cash price and the initial deposit in hire purchase is known as ?

Answers

The difference between the cash price and the initial deposit in hire purchase is known as $_$ \text{Principal} $_$ .

In hire purchase transactions, buyers can acquire goods by making an initial down payment and paying the remaining amount in installments. The difference between the total cost of the item and the initial deposit is a crucial concept known as the $_$ \text{Principal} $_$ in mathematical terms. Let's explore this in detail.

In the context of hire purchase, the total cost of the item is often referred to as the cash price. It represents the actual value of the item without considering any interest or finance charges. On the other hand, the initial deposit, also called the down payment, is the amount paid upfront by the buyer to secure the item.

Now, let's introduce some variables to help us understand this concept mathematically:

- Let CP be the cash price of the item.

- Let D be the initial deposit made by the buyer.

The difference between the cash price and the initial deposit is given by:

$\text{Principal} = CP - D$

The Principal is the amount that remains to be paid off in installments, and it serves as the basis for calculating the subsequent monthly or periodic payments in a hire purchase agreement.

The Principal is critical because it determines the total amount the buyer will end up paying for the item. It also affects the duration of the hire purchase agreement, as the buyer's installments are typically spread over a specific number of months or years.

To know more about Hire purchase here

brainly.com/question/32943538

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HirePurchaseagreement

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For one child, a childcare facility charges $350 per month for preschool and $5.00 per hour for each additional hour for after-school care. The function below can be used to determine f(h), the monthly fee for after-school care and preschool, where h represents the number of hours spent in after-school care.f(h) = 350 + 5h

If the total monthly bill for one child was $750, what was the total number of hours the child spent in after-school care?

A.100
B.90
C.88
D.80

Answers

Answer:

D.) 80

Step-by-step explanation:

750 - 350 = 400

400/5 = 80

80 hours

Hopefully this helps you :)

pls mark brainlest ;)

Answer:

D-80

Step-by-step explanation:

750-350=400

400/5=80

Solve m^2+8m=-3 by completing the square

Answers

i hope this helps you!!! be safe

Please help! Thank youu

Answers

Answer:

Step-by-step explanation:

(0, 4) (2, 0)

(0-4)/(2-0) = -4/2 = -2

y - 4 = -2(x - 0)

y - 4 = -2x + 0

y = -2x + 4

A solid is composed of squares and equilateral triangles. Its net is shown below: The area of each triangle is 16 square units. The surface area of the triangular prism is _____ square units. (Input whole number only)