Answer:
Probability to get tails exactly 8 times or exactly 5 times is 0.29
Step-by-step explanation:
No of ways the coins lands tails exactly 8 times
P(8) = 15C8 × ×
No of ways the coin lands tails exactly 5 times
P(5) = 15C5 × ×
Probability to get tails exactly 8 times or 5 times
P(8)+P(5) = 15C8 × + 15C5 ×
P = ( 15C8 + 15C5 )
P = ( (
) + (
) )
P = ( 6435 + 3003 )
P = ( 9438)
P = ( 4719)
P =
P = 0.29
Answer:
We conclude that the average calorie content of a 12-ounce can is greater than 120 calories.
Step-by-step explanation:
We are given that a quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates.
Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories.
<u><em>Let </em></u><u><em> = average calorie content of a 12-ounce can.</em></u>
So, Null Hypothesis, :
120 calories {means that the average calorie content of a 12-ounce can is less than or equal to 120 calories}
Alternate Hypothesis, :
> 120 calories {means that the average calorie content of a 12-ounce can is greater than 120 calories}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample average calories per can = 124 calories
s = sample standard deviation = 6 calories
n = sample of cans = 10
So, <em><u>test statistics</u></em> = ~
= 2.108
The value of t test statistics is 2.108.
<em>Now, at 0.05 significance level </em><em>the t table gives critical value of 1.833 at 9 degree of freedom for right-tailed test</em><em>. Since our test statistics is more than the critical values of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which </em><u><em>we reject our null hypothesis</em></u><em>.</em>
Therefore, we conclude that the average calorie content of a 12-ounce can is greater than 120 calories.