Questions: The probability of tails of a weighted coin is 0.65. The number of tails is noted each of the 15 times the coin is tossed. If this procedure is repeated 100 times, what type of distribution is simulated? A sampling distribution of the sample proportion with n=15 and p=0.65 A sampling distribution of the sample proportion with n=100 and p=0.65 A binomial distribution with n=15 and p=0.65 A binomial distribution with n=2 and p=0.65 There is not enough information to determine the type of distribution.

The probability of tails of a weighted coin is 0.65. The number of tails is noted each of the 15 times the coin is tossed. If this procedure is repeated 100 times, what type of distribution is simulated?

A sampling distribution of the sample proportion with n=15 and p=0.65

A sampling distribution of the sample proportion with n=100 and p=0.65

A binomial distribution with n=15 and p=0.65

A binomial distribution with n=2 and p=0.65

There is not enough information to determine the type of distribution.

Transcript text: The probability of tails of a weighted coin is 0.65 . The number of tails is noted each of the 15 times the coin is tossed. If this procedure is repeated 100 times, what type of distribution is simulated? A sampling distribution of the sample proportion with $n=15$ and $p=0.65$ A sampling distribution of the sample proportion with $n=100$ and $p=0.65$ A binomial distribution with $\mathrm{n}=15$ and $\mathrm{p}=0.65$ A binomial distribution with $n=2$ and $p=0.65$ There is not enough information to determine the type of distribution.

Solution

Solution Steps

Step 1: Identify the given parameters

The probability of tails ($ p $) is $ 0.65 $. The coin is tossed $ 15 $ times in each trial, and this procedure is repeated $ 100 $ times.

Step 2: Determine the type of distribution for a single trial

For a single trial of $ 15 $ coin tosses, the number of tails follows a binomial distribution with parameters $ n = 15 $ and $ p = 0.65 $. This is because each toss is independent, and there are only two possible outcomes (tails or not tails).

Step 3: Analyze the repeated trials

When the procedure is repeated $ 100 $ times, the distribution of the sample proportion of tails across these trials forms a sampling distribution of the sample proportion. The parameters for this sampling distribution are $ n = 15 $ (the number of trials in each sample) and $ p = 0.65 $ (the probability of tails).

Step 4: Match the correct option

The correct option is: A sampling distribution of the sample proportion with $ n = 15 $ and $ p = 0.65 $.