# Question

The following data represent the running lengths (in minutes) of the winners of the Academy Award for Best Picture for the years 2004–2009.

2004: Million Dollar Baby ..... 132

2005: Crash ........... 112

2006: The Departed ........ 151

2007: No Country for Old Men .... 122

2008: Slumdog Millionaire ....... 120

2009: The Hurt Locker ........ 131

(a) Compute the population mean, µ.

(b) List all possible samples with size n = 2. There should be 6C2 = 15 samples.

(c) Construct a sampling distribution for the mean by listing the sample means and their corresponding probabilities.

(d) Compute the mean of the sampling distribution.

(e) Compute the probability that the sample mean is within 5 minutes of the population mean running time.

(f ) Repeat parts (b)–(e) using samples of size n = 3. Comment on the effect of increasing the sample size.

2004: Million Dollar Baby ..... 132

2005: Crash ........... 112

2006: The Departed ........ 151

2007: No Country for Old Men .... 122

2008: Slumdog Millionaire ....... 120

2009: The Hurt Locker ........ 131

(a) Compute the population mean, µ.

(b) List all possible samples with size n = 2. There should be 6C2 = 15 samples.

(c) Construct a sampling distribution for the mean by listing the sample means and their corresponding probabilities.

(d) Compute the mean of the sampling distribution.

(e) Compute the probability that the sample mean is within 5 minutes of the population mean running time.

(f ) Repeat parts (b)–(e) using samples of size n = 3. Comment on the effect of increasing the sample size.

## Answer to relevant Questions

In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, . . . , 36. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot ...n = 300, p = 0.7 According to a study done by Wakeﬁeld Research, the proportion of Americans who can order a meal in a foreign language is 0.47. (b) In the sample obtained in part (a), what is the probability the proportion of Americans ...(a) 90% of all teenagers aged 13 to 17 have never been prescribed medication for ADHD? (b) 95% of all teenagers aged 13 to 17 have never been prescribed medication for ADHD? One question asked in the General Social Survey was this: “How many e-mails do you send in a day?” The results of 928 respondents indicate that the mean number of e-mails sent in a day is 10.4, with a standard deviation ...Post your question

0