Need help with the second part of my packet. 6. A radar unit is used to measure

Question

Need help with the second part of my packet.

6. A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. The fastest 5% of drivers may be considered to be driving recklessly. At what speed would a car be considered reckless? (10 points) a. b. The middle 90% of cars are driving between which two speeds? (10 points) Complete the following statements about sampling distributions: the standard deviation_and the shape of distribution becomes As the sample size decreases, the standard deviationand the shape of the distribution becomes 7. As the sample size increases, . Also as the sample size increases, the value of the mean becomes closer to that of the mean. (6 points) When dealing with sampling distributions, does an unusual value have a greater effect on the mean of a small sample or a large sample? Use complete sentences to explain your answer. (5 points) 8. The amount of saturated fat in a daily serving of a particular brand of breakfast cereal is normally distributed with mean 25 g and standard deviation 4 g. 9. Find the sampling distribution of the daily average saturated fat intake over a 30-day period (one month). Include the mean and standard deviation in your answer, as well as the name of the distribution. (10 points) a. What is the probability that the average daily saturated fat intake for the month was more than 27 g? (10 points) b.

Explanation / Answer

As per the Chegg policy, we are advised to do one question at a time so i am attempting the 6th one.

6 a) z score corresponding to the top 5% of the area = 1.645

Hence,

Speed that would be considered reckless = 90 + 1.645(10) = 106.45

So,

Speed of 106.45 km/ hr or more would be considered reckless.

b) z scores covering middle 90% of the area = -1.645, 1.645

Hence,

Lower bound of speed = 90 - 1.645(10) = 73.55

Upper bound of speed = 90 + 1.645(10) = 106.45

So,

90% of the speeds will fall between 73.55 km/ hr and 106.45 km/ hr.

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