Solve the inequality

The sample mean is x = 12.8%. let x be a random variable that represents the percentage of wheat crop in that county lost to hai

katen-ka-za [31]

Given that $\bar{x}=12.8\%$ and $\sigma=5.0\%$ , given that the population mean is $\mu=11\%$ and the sample size is n = 16, the test statistic is given by

$z= \frac{\bar{x}-\mu}{\sigma/\sqrt{n}} \\ \\ = \frac{12.8-11}{5/\sqrt{16}} \\ \\ = \frac{1.8}{5/4} = \frac{1.8}{1.25} \\ \\ =1.44 \\ \\ \Rightarrow p-value=p(z\ \textgreater \ 1.44) \\ \\ =1-P(z\ \textless \ 1.44)=1-0.92507 \\ \\ =0.07493$

Since the test is a two tailed test, the p-value is 2(0.07493) = 0.14986

Since the p-value is greater the significant level of α = 0.01, thus, we fail to reject the null hypothesis and conclude that there is no sufficient evidence that <span>the percentage of wheat crop lost to hail in that county is different from the national mean of 11%</span>.

8 0

3 years ago

A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or

Artyom0805 [142]

Answer:

The probability is 0.000495

Step-by-step explanation:

As per the question:

Total no. of cards in a deck = 52

No. of spades in a deck = 13

Now, we have to select 5 cards in a deck such that they belong to the same suit, i.e., spades.

The no. of ways of selecting 5 cards from a deck = $^{52}C_{5} = \frac{52!}{5!(52 - 5)!} = \frac{52!}{5!47!}$

The no. of ways of selecting 5 cards from 13 spade cards = $^{13}C_{5} = \frac{13!}{5!(13 - 5)!} = \frac{13!}{5!8!}$

Now,

Probability that the selected 5 cards are all spades, P(E) = $\frac{No.\ of\ ways\ of\ selecting\ 5\ cards\ from\ 13\ spade\ cards}{No.\ of\ ways\ of\ selecting\ 5\ cards\ from\ a\ deck}$

P(E) = $\frac{^{13}C_{5}}{^{52}C_{5}}$

P(E) = $\frac{\frac{13!}{5!8!}}{\frac{52!}{5!52!}}$

P(E) = $\frac{\frac{13\times 12\times 11\tiems 10\times 9}{5\times 4\times 3\times 2\times 1}}{\frac{52\times 51\times 50\times 49\times 48}{5\times 4\times 3\times 2\times 1}}$

P(E) = $\frac{13\times 12\times 11\tiems 10\times 9}{52\times 51\times 50\times 49\times 48} = 4.95\times 10^{- 4} = 0.000495$

7 0

2 years ago

The most common Native American language used in 2010 is Navajo, with about 169,000 people speaking the language nationally. If

Diano4ka-milaya [45]

169,000/308,700,000 which can be simplified to 169/308,700 and decimal form just divide 169,000 by 308,700,000 and you get .0005474571, and percentage multiply the decimal by 100 so you get .055% (rounded)

4 0

3 years ago

Read 2 more answers

virgil has 1/6 of a bday cake left over. he wants to share with 3 friends. what fraction of the original cake will each of the f

Tpy6a [65]

1/6 divided by 4 = 1/24
so each person would get 1/24 of that cake
(just wondering what would the flavor of the cake be??)

3 0

2 years ago

What is the congruence theorem used to prove that the two triangles are congruent?

natka813 [3]

Answer:

AAS, the two equal angles, the two right triangles, and the shared side