problem types from lec 16 - the normal distribution\nx to area, shaded left +\nx to area, shaded right +\nx…

problem types from lec 16 - the normal distribution\nx to area, shaded left +\nx to area, shaded right +\nx to area, shaded between +\nx to area, percentile +\narea to x, shaded left +\narea to x, shaded right +\narea to x, shaded between +\n\naccording to a recent national survey, the mean number of hours that adult americans watch netflix each week is 15.13 hours with a standard deviation of 6.51 hours. if a random sample of 36 adult americans is selected, what is the probability that their mean number of hours watching netflix each week is less than 17 hours.\n\nproblem type: select an answer select an answer\nmean:\nstandard deviation:\nfinal answer(s):\nif there are two answers, list both answers separated by a comma.

problem types from lec 16 - the normal distribution\nx to area, shaded left +\nx to area, shaded right +\nx to area, shaded between +\nx to area, percentile +\narea to x, shaded left +\narea to x, shaded right +\narea to x, shaded between +\n\naccording to a recent national survey, the mean number of hours that adult americans watch netflix each week is 15.13 hours with a standard deviation of 6.51 hours. if a random sample of 36 adult americans is selected, what is the probability that their mean number of hours watching netflix each week is less than 17 hours.\n\nproblem type: select an answer select an answer\nmean:\nstandard deviation:\nfinal answer(s):\nif there are two answers, list both answers separated by a comma.

Answer

Answer:

0.9463

Explanation:

Step1: Identify sampling distribution stats

Population mean $\mu = 15.13$, population standard deviation $\sigma = 6.51$, sample size $n=36$. Sampling mean $\mu_{\bar{x}} = \mu = 15.13$ Standard error $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{6.51}{\sqrt{36}} = 1.085$

Step2: Calculate z-score

$z = \frac{\bar{x} - \mu_{\bar{x}}}{\sigma_{\bar{x}}} = \frac{17 - 15.13}{1.085} \approx 1.72$

Step3: Find cumulative probability

Use z-table for $z=1.72$, cumulative left-tail area = 0.9463