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sweet [91]
3 years ago
10

Let x denote the courtship time for a randomly selected female–male pair of mating scorpion flies (time from the beginning of in

teraction until mating). suppose the mean value of x is 120 min and the standard deviation of x is 110 min (suggested by data in the article
Mathematics
1 answer:
gavmur [86]3 years ago
6 0

Complete Question:

a) Is it plausible that X is normally distributed?

b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 100 min and 125 min?

Answer:

a) It is plausible that X is normally distributed

b) probability that the sample mean courtship time is between 100 min and 125 min is 0.5269

Step-by-step explanation:

a)X denotes the courtship time for the scorpion flies which indicates that is a real - valued random variable, and since normal distribution is a continuous probability distribution for a real valued random variable, it is plausible that X is normally distributed.

b) Probability that the sample mean courtship time is between 100 min and 125 min

\mu = 120\\n = 50

P(x_{1}  < \bar{X} < x_{2} ) = P(z_{2}  < \frac{x_{2}- \mu }{SD} ) - P(z_{1}  < \frac{x_{2}- \mu }{SD})

SD = \sqrt{\frac{\sigma^{2} }{n} } \\SD = \sqrt{\frac{110^{2} }{50} } \\SD = 15.56

P(100 < \bar{X}

From the probability distribution table:

P(z_{2}  < 0.32 ) = 0.6255\\ P(z_{1}  < -1.29) = 0.0986

P(100 < \bar{X}

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