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timofeeve [1]
2 years ago
8

Harriet has £600.

Mathematics
2 answers:
Mrac [35]2 years ago
4 0

Answer:

£210

Step-by-step explanation:

1/4 of 600= 150

2/5 of 600= 240

240 + 150= 390

600 - 390 = 210

She has £210 left

galina1969 [7]2 years ago
3 0
7/20 is the fraction she has left.

1/4 + 2/5= 13/20 she has spent so she has 7/20 left.
You can also check this by adding the 150 + 240 = 390 she has spent and 210 she left to spend. 210/600 = 7/20
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An article reports that 1 in 500 people carry the defective gene that causes inherited colon cancer. In a sample of 2500 individ
Ne4ueva [31]

Answer:

The approximate distribution of the number who carry this gene is approximately normal with mean \mu = 5 and standard deviation \sigma = 2.23

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they carry the defective gene that causes inherited colon cancer, or they do not. The probability of a person carrying this gene is independent from other people. So the binomial probability distribution is used to solve this question.

A sample of 2500 individuals is quite large, so we use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

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 = \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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

An article reports that 1 in 500 people carry the defective gene that causes inherited colon cancer.

This means that p = \frac{1}{500} = 0.002

In a sample of 2500 individuals, what is the approximate distribution of the number who carry this gene?

n = 2500

So

\mu = E(X) = np = 2500*0.002 = 5

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2500*0.002*0.998} = 2.23

So the approximate distribution of the number who carry this gene is approximately normal with mean \mu = 5 and standard deviation \sigma = 2.23

4 0
3 years ago
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