Using the normal distribution, it is found that the proportion of guests that will spend between 28 and 37 minutes in the house is:
0.6514.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.In the context of this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 35, \sigma = 4[/tex]
The proportion of guests that will spend between 28 and 37 minutes in the house is the p-value of Z when X = 37 subtracted by the p-value of Z when X = 28, hence:
X = 37:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (37 - 35)/4
Z = 0.5
Z = 0.5 has a p-value of 0.6915.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (28 - 35)/4
Z = -1.75
Z = -1.75 has a p-value of 0.0401.
Then the proportion is:
0.6915 - 0.0401 = 0.6514.
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Thirty-nine percent of consumer prefer to order their prescription remotely instead of going to the Pharmacy. They argue that going in in person prompt individual to purchase other items that they did not need, especially those chocolate candies by the register. If ordering prescription remotely follows a binomial distribution pattern. You randomly select 10 consumers. Find the probability that the number of customers who prefer to shop to order prescription remotely is:
The solutions to the problems concerning the order of the prescription remotely are:
The probability of exactly 4 is 0.25The probability of at most 2 is 0.18How to solve for the probabilityWe have to solve this by making use of binomial probability
where p is the probability
x is the number of success
n is the trials
We have to find the probability of exactly 4
We have to solve this by making use of the binomial distribution formula
= [tex]nCxP^{x} (1-p)^{n-4}[/tex]
where n = 10
x = 4
p = 39
39/100 = 0.39
percentage = 0.39
When we put these values in the formula that we have here we would have
[tex]10C_{4} P^{4}(1-P)^{10-4}[/tex]
This would be written as
[tex]\frac{10!}{4!(10-4)! } *0.39^{4} *(1-0.39)^6[/tex]
Probability of exactly 4 = 210 * 0.39⁴ * (1 - 0.39)⁶
= 0.25
The probability of exactly 4 is 0.25
2. We have to solve for the probability of at most 2
= probability of exactly 1 + probability of exactly 2
= ₁₀C₁ * p¹ * (1 - p)¹⁰ ⁻¹ + ₁₀C₂ * P² * (1 - P)¹⁰⁻²
= 10 * 0.39¹ * 1 - 0.39⁹ + 45 * 0.39² * 1 - 0.39⁸
Probability of at most 2 = 10 * 0.39 * (1 - 0.39)⁹ + 45 * 0.39² * (1 - 0.39)⁸
= 0.18
The probability of at most 2 is 0.18
The probability that the number of customers that prefers remote order is exactly 4 is 0.25, while the probability that they are exactly 2 is 0.18
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complete question
Thirty-nine percent of consumer prefer to order their prescription remotely instead of going to the Pharmacy. They argue that going in in person prompt individual to purchase other items that they did not need, especially those chocolate candies by the register. If ordering prescription remotely follows a binomial distribution pattern. You randomly select 10 consumers. Find the probability that the number of customers who prefer to shop to order prescription remotely is:
Exactly 4 (Show all work – Formula and calculations)
At most 2 (Show all work – Formula and calculations)
Where are most heavier metals, such as iron and nickel, found in the Earth's layers and why?
Answer:
The Mantle
Explanation:
The Mantle: The mantle is the thickest layer of the Earth, making up about 82% of its volume. The mantle is composed primarily of heavy metals, such as iron, nickel, magnesium, and others. Scientists describe the state of the mantle as 'plastic.