It has been claimed that 70% of all single men would welcome awoman taking the i

Question

It has been claimed that 70% of all single men would welcome awoman taking the initiative in asking for a date. A random sampleof 20 single men were asked if they would welcome a woman takingthe initiative in asking for a date. A. What type of distribution is this? Write the probabilitydistribution formula of the random variable r with the giveninformation. B. What is the probability that at least 17 of the men willsay yes? C. What is the probability that fewer than 4 of the men sayyes? D. What is the probability that none of the men say yes? E. What is the mean number of men that will say yes? Interpretthe mean. It has been claimed that 70% of all single men would welcome awoman taking the initiative in asking for a date. A random sampleof 20 single men were asked if they would welcome a woman takingthe initiative in asking for a date. A. What type of distribution is this? Write the probabilitydistribution formula of the random variable r with the giveninformation. B. What is the probability that at least 17 of the men willsay yes? C. What is the probability that fewer than 4 of the men sayyes? D. What is the probability that none of the men say yes? E. What is the mean number of men that will say yes? Interpretthe mean.

Explanation / Answer

B. Probability of 17 + 18 + 19 +20. 20 = .7^20 19 = .7^19 * .3^1 * 20 18 = .7^18 * .3^2 * 20 * 19 17 = .7^17 * .3^3 * 20 * 19 * 18
Total = .492951
C. Probability of 3,2,1,0. 0 = ~0 1 = .3^19 * .7^1 * 20 2 = .3 ^ 18 * .7 ^ 2 * 20 * 19 3 = .3 ^ 17 * .7 ^ 3 * 20 * 19 * 18
Total: .0000003 = ~0 D. Probability of 0 = .3^20 = ~0(.000000000034868)
E. Mean = .7 * 20 = 14. On average, 14 men out of20 will welcome a woman taking the initiative in asking for adate.

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