Respuesta :
The probability that the top card is spades in more than 30% of the sample in a nontraditional deck of cards is 0.224.
How to get the z scores?
If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
[tex]Z = \dfrac{X - \mu}{\sigma}, \\[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
A nontraditional deck of cards has 30 total cards: 5 hearts, 10 clubs, 8 spades, and 7 diamonds. the cards are shuffled, and the top card is noted. this process is repeated 100 times.
Here, the sample size n is 100. IN the 30 cards 8 cards are spades. Thus, the probability of a card to be spade is,
[tex]P=\dfrac{8}{30}\\P=0.2667[/tex]
Thus, the mean of it is,
[tex]\mu=100\times0.2667\\\mu=26.67[/tex]
The value of standard deviation is,
[tex]\sigma=\sqrt{\mu(1-p)}\\\sigma=\sqrt{26.67(1-0.2667)}\\\sigma=4.42[/tex]
Now for the P(X>30), z-score is,
[tex]Z=\dfrac{x-\mu}{\sigma}\\Z=\dfrac{30-26.67}{4.42}\\Z=0.754\\P(Z > 0.754)=0.224[/tex]
Thus, the probability that the top card is spades in more than 30% of the sample in a nontraditional deck of cards is 0.224.
Learn more about the z score here;
https://brainly.com/question/13299273
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