The following 5 questions are based on this information. A software company\'s a
ID: 3356874 • Letter: T
Question
The following 5 questions are based on this information. A software company's average daily stock price last year is $38.12 (µ). The population standard deviation () for those prices is $2.45. Let X be a random variable denoting stock prices. We plan to take a random sample of 32 days. Question 17 Not yet answered Points out of 1.00 Flag question Question text What is the sampling distribution of X ¯ X¯ when a sample of size 32 is used? Select one: a. Is normal due to the Central Limit Theorem b. Is not normal because the sample size is too small c. Is normal due to the Chebyshev’s Theorem d. Is not normal because the sample size is too large Question 18 Not yet answered Points out of 1.00 Flag question Question text Suppose that we now reduce the sample size from 32 to 12. The sampling distribution of X ¯ X¯ will be normal only if Select one: a. X has a normal distribution b. X has a uniform distribution c. X has a skewed distribution d. X has a bi-modal distribution Question 19 Not yet answered Points out of 1.00 Flag question Question text What is the probability that a random sample of 32 days will provide an average stock price ( X ¯ X¯ ) that is more than $39? Select one: a. 98% b. 64% c. 36% d. 2% Question 20 Not yet answered Points out of 1.00 Flag question Question text What is the probability that a random sample of 32 days will provide an average stock price ( X ¯ X¯ ) that is within $0.50 of the population mean ( )? Select one: a. 88% b. 75% c. 25% d. 12% Question 21 Not yet answered Points out of 1.00 Flag question Question text The probability in the PRECEDING question would _________if we were to increase the sample size to 64. Select one: a. stay the same b. decrease c. increase d. be zero
Explanation / Answer
17) a. Is normal due to the Central Limit Theorem
18) a. X has a normal distribution
19)
here std error =std deviation/(n)1/2 =0.4331
hence P(X>39)=P(Z>(39-38.12)/0.4331)=P(Z>2.032)=2%
option d 2%
20)
P(-0.5/0.4331<Z<0.5/0.4331)=P(-1.1545<Z<1.1545)=0.8758-0.1242 =0.7517 ~ 75%
option b. 75%
21) The probability in the PRECEDING question would increase option c