Probability.

Mathematics

1 answer:

swat323 years ago

5 0

Answer: 0.0386

Step-by-step explanation:

Given: The probability hat the frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked : p= 0.30

Sample size : n = 12

Let x = Number of contaminated chickens

Here , two outcomes for any chicken (either contaminated or not) , so it follows binomial distribution.

Binomial probability formula:

$P(X=x) = \ ^nC_x p^x(1-p)^{n-x}$

The probability that the consumer will have more than 6 contaminated chickens :-

$P(X>6)=P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)+P(X=12)\\\\=^{12}C_6(0.3)^6(0.7)^6+^{12}C_7(0.3)^7(0.7)^5+^{12}C_8(0.3)^8(0.7)^4+^{12}C_9(0.3)^9(0.7)^3+^{12}C_{10}(0.3)^{10}(0.7)^2+^{12}C_{11}(0.3)^{11}(0.7)^1+^{12}C_0(0.3)^{12}(0.7)^0$

$=0.03860084306\approx0.0386$ (simplified)

Hence, the required probability = 0.0386

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Calvin had 30 minutes in time-out. For the first 23 1/3 minutes, Calvin counted spots on the ceiling. For the rest of the time,

scoundrel [369]

Answer: $\frac{20}{3}\ minutes$ or $6 \frac{2}{3}\ minutes$

Step-by-step explanation:

For this exercise you can convert the mixed number to an improper fraction:

1. Multiply the whole number part by the denominator of the fraction.

2. Add the product obtained and the numerator of the fraction (This will be the new numerator).

3. The denominator does not change.

Then:

$23\frac{1}{3}= \frac{(23*3)+1}{3}= \frac{70}{3}\ minutes$

You know that he had 30 minutes in time-out, he counted spots on the ceiling for $\frac{70}{3}$ minutes and the rest of the time he made faces at his stuffed tiger.