Mathematics, 09.04.2020 04:34 kloeydrea08

. Suppose that a random sample of n = 102 children is selected from the population of newborn infants in Mexico. The probability that a child in this population weighs at most 2500 grams is presumed to be π = 0.15. Calculate the probability that thirteen or fewer of the infants weigh at m

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Answer from: artursino

30.85% probability that thirteen or fewer of the infants weigh at most 2500 grams

Step-by-step explanation:

I am going to 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

n = 102, p = 0.15

$\mu = E(X) = 102*0.15 = 15.3$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{102*0.15*0.85} = 3.61$

Calculate the probability that thirteen or fewer of the infants weigh at most 2500 grams

This is $P(X \leq 13)$ , which using continuity correction is $P(X \leq 13 + 0.5) = P(X \leq 13.5)$ , which is the pvalue of Z when X = 13.5.

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

$Z = \frac{13.5 - 15.3}{3.61}$

Z = -0.5

Z = -0.5 has a pvalue of 0.3085

30.85% probability that thirteen or fewer of the infants weigh at most 2500 grams

Answer from: Quest

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.

Answer from: Quest

see below

step-by-step explanation:

x+2> 6

subtract 2 from each side

x+2-2 > 6-2

x > 4

there is an open circle at 4 since is it is greater than and the line goes to the right

Which graph represents the solution set of the inequality x+2> 6

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