Un vendedor de frutas tiene cierto número de mangos, vende 3/5 de ellos más dos mangos; luego vende 1/3 de los restantes más dos
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4 larger door can be cut for a board that is 10.5 feet long
Step-by-step explanation:
The given is:
- Doors for the small cabinets are 11.5 inches long
- Doors for the large cabinet are 2.3 time as long as the door for a small cabinet
- There is a board that is 10 1/2 feet long
We need to find how many larger door can be cut from the board
∵ 1 foot = 12 inches
∵ The board is feet long
∵ feet =
× 12 = 126 inches
∵ The small door is 11.5 inches long
∵ The larger door is 2.3 times as long as the small door
∴ The larger door = 11.5 × 2.3 = 26.45 inches long
Divide the length of the board by the length of the larger door to find
how many larger door can be cut from the board
∵ The length of the board = 126 inches
∵ The length of the larger door = 26.45 inches
∵ 126 ÷ 26.45 = 4.76
∴ 4 larger doors can be cut from the board
4 larger door can be cut for a board that is 10.5 feet long
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Answer:
0.2643 = 26.43% probability that the proportion of freshmen who have had their wisdom teeth removed is greater than the proportion of seniors.
Step-by-step explanation:
To solve this question, we need to understand the normal distribution, the central limit theorem, and subtraction of normal variables.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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 normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Subtraction of normal variables:
When we subtract normal variables, the mean of the subtraction will be the subtraction of the means, while the standard deviation will be the square root of the sum of the variances.
In a large local high school, 19% of freshmen have had their wisdom teeth removed. Sample of 60 freshmen:
So, by the central limit theorem:
24% of seniors have had their wisdom teeth removed. Sample of 50 seniors.
So, by the central limit theorem:
What is the probability that the proportion of freshmen who have had their wisdom teeth removed is greater than the proportion of seniors?
This is the probability that the subtraction of the proportion of freshmen by the proportion of seniors is larger than 0. For this distribution, we have that:
This probability is 1 subtracted by the pvalue of Z when X = 0. So
By the Central Limit Theorem
has a pvalue of 0.7357
1 - 0.7357 = 0.2643
0.2643 = 26.43% probability that the proportion of freshmen who have had their wisdom teeth removed is greater than the proportion of seniors.