Question

Suppose x has a distribution with a mean of 70 and a standard deviation of 20. Random samples of size n = 64 are drawn. (a) Describe the distribution. x has a geometric distribution. has a normal distribution. x has an unknown distribution. x has a Poisson distribution. X has an approximately normal distribution. x has a binomial distribution. Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) Hy = Oz = (b) Find the z value corresponding to x = 75. (Enter an exact number.) z = (c) Find P(x < 75). (Enter a number. Round your answer to four decimal places.) P(x < 75) = (d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 75? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 75. No, it would not be unusual because more than 5% of all such samples have means less than 75. Yes, it would be unusual because more than 5% of all such samples have means less than 75. Yes, It would be unusual because less than 5% of all such samples have means less than 75.

Answer 1

soluton! Given that u= 70 o= 20 na 64 as X has a normal distribution u=10 l= lx = 70 2.5 20 In 1648 ex=yo i = 2 .5 o b) x = 75 2-7-17 2 = 75-10 . 25 2 =21 2=21

c) P (X (75)=P(X-M² ( 75-70) 2 .5 - P ( 222) = 0.9772 than d) No, it would not be unstsuch because 5% of all such samples have means than 75 more Jess.