QuestionJuly 15, 2025

Show all values of n, p, and x for full credit! A recent study shows that 60% of all adults in the U.S. favor tougher gun laws. 1. If you survey 13 random adults, what is the probability that exactly 5 favor tougher gun laws? 2. If you survey 9 random adults, what is the probability that more than five favor tougher gun laws? 3. If you survey 14 random adults, what is the probability that 9 or fewer favor tougher gun laws? 4. If you survey 8 random adults, what is the probability that between 4 and 7 of them (inclusive) favor tougher gun laws?

Show all values of n, p, and x for full credit! A recent study shows that 60% of all adults in the U.S. favor tougher gun laws. 1. If you survey 13 random adults, what is the probability that exactly 5 favor tougher gun laws? 2. If you survey 9 random adults, what is the probability that more than five favor tougher gun laws? 3. If you survey 14 random adults, what is the probability that 9 or fewer favor tougher gun laws? 4. If you survey 8 random adults, what is the probability that between 4 and 7 of them (inclusive) favor tougher gun laws?
Show all values of n, p, and x for full credit! A recent study shows that 60% of all adults in the U.S. favor tougher gun laws. 1. If you survey 13 random adults, what is the probability that exactly 5 favor tougher gun laws? 2. If you survey 9 random adults, what is the probability that more than five favor tougher gun laws? 3. If you survey 14 random adults, what is the probability that 9 or fewer favor tougher gun laws? 4. If you survey 8 random adults, what is the probability that between 4 and 7 of them (inclusive) favor tougher gun laws?

Solution
4.0(351 votes)

Answer

1. P(X = 5) \approx 0.231 ### 2. P(X > 5) \approx 0.382 ### 3. P(X \leq 9) \approx 0.764 ### 4. P(4 \leq X \leq 7) \approx 0.819 Explanation 1. Define the Binomial Distribution Parameters For each scenario, define n (number of trials), p (probability of success), and x (number of successes). 1. n = 13, p = 0.6, x = 5 2. n = 9, p = 0.6, x > 5 3. n = 14, p = 0.6, x \leq 9 4. n = 8, p = 0.6, 4 \leq x \leq 7 2. Apply the Binomial Probability Formula Use the formula for binomial probability: P(X = x) = \binom{n}{x} p^x (1-p)^{n-x}. 1. Calculate P(X = 5) for n = 13, p = 0.6, x = 5. 2. Calculate P(X > 5) for n = 9, p = 0.6. This is 1 - P(X \leq 5). 3. Calculate P(X \leq 9) for n = 14, p = 0.6. 4. Calculate P(4 \leq X \leq 7) for n = 8, p = 0.6. This is P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7). 3. Compute Each Probability Use a calculator or software to compute the probabilities accurately. 1. P(X = 5) = \binom{13}{5} (0.6)^5 (0.4)^8 2. P(X > 5) = 1 - \sum_{x=0}^{5} \binom{9}{x} (0.6)^x (0.4)^{9-x} 3. P(X \leq 9) = \sum_{x=0}^{9} \binom{14}{x} (0.6)^x (0.4)^{14-x} 4. P(4 \leq X \leq 7) = \sum_{x=4}^{7} \binom{8}{x} (0.6)^x (0.4)^{8-x}

Explanation

1. Define the Binomial Distribution Parameters<br /> For each scenario, define $n$ (number of trials), $p$ (probability of success), and $x$ (number of successes).<br /><br />1. $n = 13$, $p = 0.6$, $x = 5$<br />2. $n = 9$, $p = 0.6$, $x > 5$<br />3. $n = 14$, $p = 0.6$, $x \leq 9$<br />4. $n = 8$, $p = 0.6$, $4 \leq x \leq 7$<br /><br />2. Apply the Binomial Probability Formula<br /> Use the formula for binomial probability: $P(X = x) = \binom{n}{x} p^x (1-p)^{n-x}$.<br /><br />1. Calculate $P(X = 5)$ for $n = 13$, $p = 0.6$, $x = 5$.<br />2. Calculate $P(X > 5)$ for $n = 9$, $p = 0.6$. This is $1 - P(X \leq 5)$.<br />3. Calculate $P(X \leq 9)$ for $n = 14$, $p = 0.6$.<br />4. Calculate $P(4 \leq X \leq 7)$ for $n = 8$, $p = 0.6$. This is $P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)$.<br /><br />3. Compute Each Probability<br /> Use a calculator or software to compute the probabilities accurately.<br /><br />1. $P(X = 5) = \binom{13}{5} (0.6)^5 (0.4)^8$<br />2. $P(X > 5) = 1 - \sum_{x=0}^{5} \binom{9}{x} (0.6)^x (0.4)^{9-x}$<br />3. $P(X \leq 9) = \sum_{x=0}^{9} \binom{14}{x} (0.6)^x (0.4)^{14-x}$<br />4. $P(4 \leq X \leq 7) = \sum_{x=4}^{7} \binom{8}{x} (0.6)^x (0.4)^{8-x}$
Click to rate:

Similar Questions