We use a t distribution for inference about a population mean instead of the standard Normal distribution:

Mathematics

1 answer:

Basile [38]3 years ago

3 0

Answer: d. if we do not know the population standard deviation and must use the sample standard deviation.

Step-by-step explanation:

We use t-distribution is quite similar to distribution of z-score .

The interpretation of t-scores and z-scores are same.

T- distribution is used when the data is not accurately normal and when the population standard deviation is unknown.

In the absence of population standard deviation , we use the standard deviation of the sample.

So , We use a t distribution for inference about a population mean instead of the standard Normal distribution if we do not know the population standard deviation and must use the sample standard deviation.

Hence, the correct option is : d. if we do not know the population standard deviation and must use the sample standard deviation.

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a. There are four 5s that can be drawn, and $\binom43=4$ ways of drawing any three of them. There are $\binom{52}3=22,100$ ways of drawing any three cards from the deck. So the probability of drawing three 5s is

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In case you're asked about the probability of drawing a 3 or a 5 (and NOT three 5s), then there are 8 possible cards (four each of 3 and 5) that interest you, with a probability of $\frac8{52}=\frac2{13}\approx0.15$ of getting drawn.

b. Similar to the second case considered in part (a), there are now 12 cards of interest with a probability $\frac{12}{52}=\frac3{13}\approx0.23$ of being drawn.

c. There are four 6s in the deck, and thirteen diamonds, one of which is a 6. That makes 4 + 13 - 1 = 16 cards of interest (subtract 1 because the 6 of diamonds is being double counted by the 4 and 13), hence a probability of $\frac{16}{52}=\frac4{13}\approx0.31$ .