Mathematics, 20.03.2020 12:52 Armendariz1

Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 200 words per minute. If 10 students are selected at random, what is the probability that at most two of them would read at less than 850 words per minute

Answers: 3

Show answers

Answers

Answer from: mv603177

36.04% probability that at most two of them would read at less than 850 words per minute

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the binomial probability distribution.

Normal probability distribution

Problems of normally distributed samples are 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.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Percentage of students who read less than 850 words per minute.

Pvalue of Z when X = 850. The mean is $\mu = 950$ and the standard deviation is $\sigma = 200$

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

$Z = \frac{850 - 950}{200}$

Z = -0.5

Z = -0.5 has a pvalue of 0.3085.

30.85 of students read less than 850 words per minute.

If 10 students are selected at random, what is the probability that at most two of them would read at less than 850 words per minute

This is $P(X \leq 2)$ when n = 10, p = 0.3085 . So

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.3085)^{0}.(0.6915)^{10} = 0.0250$

$P(X = 1) = C_{10,1}.(0.3085)^{1}.(0.6915)^{9} = 0.1115$

$P(X = 2) = C_{10,2}.(0.3085)^{2}.(0.6915)^{8} = 0.2239$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0250 + 0.1115 + 0.2239 = 0.3604$

36.04% probability that at most two of them would read at less than 850 words per minute

Answer from: Quest

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean = $\frac{2+3+4+5+6+7+8+9}{8}=\frac{44}{8}=5.5$

also, median= $\frac{5+6}{2}=\frac{11}{2}=5.5$ , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean = $\frac{2+3+4+5+6}{5}=\frac{20}{5}=4$

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

Answer from: Quest

what golf ball

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 22:30

Find the area of the region that is inside r=3cos(theta) and outside r=2-cos(theta). sketch the curves.

Answers: 3

Answer

Mathematics, 21.06.2019 22:30

Aflagpole broke in a storm. it was originally 8 1 81 feet tall. 2 8 28 feet are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground some distance away. how far away is the end of the pole from the base of the pole along the ground?

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

It takes an ant farm 3 days to consume 1/2 of an apple. at that rate, in how many days will the ant farm consume 3 apples

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

Written as a simplified polynomial in standard form, what is the result when (2x+8)^2(2x+8) 2 is subtracted from 8x^2-38x 2 −3?

Answers: 3

Answer

You know the right answer?

Students who have completed a speed reading course have reading speeds that are normally distributed...