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anzhelika [568]
3 years ago
13

In a game the player wins if he rolls a 6 on a number cube. If the number cube is rolled 18 times, then what is a reasonable pre

diction for the number of unsuccessful rolls? Show work
Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
8 0

If the number cube is rolled 18 times, then the number of unsuccessful rolls = 90 unsuccessful rolls.

<u>Step-by-step explanation</u>:

<u>step 1</u>: A cube has six faces and each face is numbered from 1 to 6.

<u>step 2</u>: The win in the game requires the number 6, when a cube is rolled.

<u>step 3</u>: On rolling a cube, the outcomes are (1,2,3,4,5, and 6).

<u>step 4</u>: Out of these outcomes, 5 are unsuccessful rolls (1,2,3,4,5) and 1 is a successful roll (6).

<u>step 5</u>: If the cube is rolled 18 times,

then the number of unsuccessful rolls = 18 * 5 unsuccessful rolls

                                                                  = 90 unsuccessful rolls.

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Answer:

a. X is a binomial random variable with n = 50 and p = 0.04

b. Y is a binomial random variable with n = 40 and p = 0.015

Step-by-step explanation:

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.

X: the number of US residents (out of 50) with blood type AB.

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States

This means that p = 0.04, n = 50

Y: the number of Australians (out of 40) with blood type AB.

In Australia, only 1.5% of the population has blood type AB.

This means that p = 0.015, n = 40

Z: the total number of individuals (out of 90) with blood type AB.

Here

n = 90, p = 0.04*\frac{50}{90} + 0.015*\frac{40}{90} = 0.0289

Which of the following is true about the random variables X, Y, and Z?

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Question 5
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The COP is 0.5

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Step-by-step explanation:

Mean = 81740

Standard deviation = 4590

Sample size = 15

Alpha level = 1-0.95 = 0.05

Df = 15-1 = 14

Critical value:

alpha/2 = 0.05/2 = 0.05

t0.025

t critical value = 2.145

Margin of error ME

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ME = 2542.09

Confidence interval

Lower CI = mean - ME

= 81740-2542.09

= 79197.91

Upper CI = mean + ME

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= 84282.09

[ 79197.91, 84282.09]

B.

Using excel, exact answer for CI

Lower limit = 79198.142724212173

Upper limit = 84281.8572757827

C.

The assumptions to be made from the population are that

1. Samples are random

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