Question

DJ NU VUJU 5. In Brooklyn half marathon, the finish time is approximately normally distributed with a mean of 190 minutes and a standard deviation of 23 minutes. If Jim fail to win 80% of runners in Brooklyn half marathon, what is the finish time that Jim complete this race? 6. The General Electric claims that 100-watt light bulbs have normal distribution with a mean of 750 hours and a standard deviation of 60 hours. Find the probability that the mean life of a random sample of 36 such bulbs will be between 725 and 748 hours. 7. A local supermarket claims the drink they produced is 12-ounce per packages. A management team want to test whether the drinks weigh is not equal to 12 ounces. The management team took a random sample of 30 such drinks and found that the mean weight of this sample is 11.964 ounces. The population follows a normal distribution with the standard deviation of 0.15 ounce. Test at the 5% significance level whether the drinks is not equal to 12-ounces. 8. A report claim that the average driving speed is 75 miles per hour in a certain highway. 60 randomly selected cars were checked by radar. The average speed was 77.40 mile per hour and standard deviation of the speed was 5.90 miles per hour. Test at the 5% significance level whether the driving speed is over 75 miles per hour in this highway.

Answer 1

Hi, We are supposed to answer one question at a time. Since, it is not mentioned which question to be answered. I am answering the 5th question. Please repost other questions separately.

Given Information:

Mean finishing time = 190 minutes

Standard Deviation = 23 minutes

It is given that Jim Failed to win 80% of the runners . We will assume the confidence interval to be 80%.

Following formula can be used to caculated the Jim's finishing time.

z = X-u where, z=z score at given confidence level X = Jim's Finishing Time u = Mean Finishing time o=Standard Deviation

Putting the given values in the above formula, we get:

The z value at 80% confidence interval is 1.282 (from standard normal table)

1.282 = X-190 X = 219.486

Therefore, Jim's finishing tiem is approx 220 minutes