Question

The average amount of nicotine in a cigarette is about 12 mg (milligrams), but for your information, when you smoke a cigarette, you only consume about 0.95 mg. We assume that nicotine distribution in cigarettes is normal with standard deviation 1.5 mg. A cigarette manufacturer claims that it has reduced the amount of nicotine in its cigarettes. You the curious cat, actually go out and take a random sample of 50 cigarettes; you find that average amount is 11.7 mg. Find the probability P(X¯≤11.7)

The average income in a city is $35,000 and the standard deviation is $7,000. Assume that the income in the city is normally distributed. Find the z-score for someone who makes $21,000 .

The average income in a city is $35,000 and the standard deviation is $7,000. Assume that the income in the city is normally distributed. Find the corresponding income for an individual if that person’s z-score is 2.

If the average income in a city is $35,000 and the standard deviation is $7,000, then find the income level that separates the bottom 5%.

If the average income in a city is $35,000 and the standard deviation is $7,000, then find the income level that separates the top 5%.

Income in a city is normally distributed with average income $35,000 and the standard deviation is $7,000. Find z-score for the top 3% earners and then convert it to actual income. What is the actual income level that separates the top 3%?

Income in a city is normally distributed with average income $35,000 and the standard deviation is $7,000. Find the z-scores for the middle 50% of earners and then convert those to actual incomes. Write the incomes separated by comma.

The incomes in Dhaka, the capital of Bangladesh, is normally distributed with mean $1,500 and standard deviation $300. Find the probability that the person makes less than $1200

The incomes in Dhaka, the capital of Bangladesh, is normally distributed with mean $1,500 and standard deviation $300. Find the probability that the person makes less than $1200

The incomes in Dhaka, the capital of Bangladesh, is normally distributed with mean $1,500 and standard deviation $300. Find the probability that the person makes between $1,200 and $1,800.

The incomes in Dhaka, the capital of Bangladesh, is normally distributed with mean $1,500 and standard deviation $300. Find the probability that the person makes exactly $1,700

The lifetime of smart phone is normally distributed with the average usable time approximately 36 months and the standard deviation of 6 months. If you want to purchase an insurance policy so that there is 15.87% chance that your phone will NOT be fixed if it is broken. What should be the length of time in months for which you should buy the insurance?

The grade point averages (GPAs) of students at your school is normally distributed with mean 3.2 and standard deviation 0.25. Your institution decides to give scholarships to students, but to be eligible to apply your GPA must be among the top 15.87% of the students. What should be your minimum GPA to be eligible to apply?

Answer 1

As per Chegg policy only first four parts have been answered

a) If N=50 and standard deviation, and if the sample mean,

so,

Z score is applicable here as

Using the Z table shown below the P-value is calculated as

P-value=0.0787

b) The Z score is calculated as

c) The corresponding value is calculated as

d) At bottom 5 % value the Z score is -1.65 which is calculated by the table is shown below hence

The income level that separate is calculated by

The Z score table is