1) The laser offset is known to have a normal distribution with population mean of 100 nm and population standard deviation of 2 nm. ii) What proportion of the laser offset will be shorter than 98 nm?

The boiling point of 16 samples of a certain brand of hydrogenated vegetable oil used in a fryer was collected, resulting in Xbar=152.1 degrees. Assume that the distribution of melting point is normal with o=3.20. If the boiling point is different than 150 degrees, then either the oil will be too hot and will burn food or it will be too cool and will not properly cook the food. Is the sample mean significantly different from the target of 150 degrees? Use alpha=0.01 Но: H1: Define critical (rejection) region(s): Calculate the appropriate test statistic: What decision do we make? What this decision means in terms of this problem?

Suppose that heights of 10-year-old boys in the US vary according to a normal distribution with mean of 138 cm and standard deviation of 7. Compute the Z-score for a boy with height of 150 cm and find the correct interpretations.   a. Boy's height is 0.71 standard deviation lower the national average   b. Boy's height is 1.71 standard deviation above the national average   c. Boy's height is 1.71 standard deviation lower than the national average   d. Boy's height is 2.71 standard deviation above the national average

2. Suppose the chamber of commerce at Pyramid Lake advertises that the average length of trout caught at the lake is μ = 19 inches. However, a fishing magazine survey reported that for a random sample of 51 fish caught, the mean length was x = 18.5 inches with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of the trout caught at Pyramid Lake is less than μ =  10 inches? (Use α = 0.05)

The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o = 0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 15 cigarettes of this brand. The sample yields an average of 1.6 mg of nicotine. Conduct a test using a significance level of a = 0.05. (a) The standardized test statistic (b) The critical value (endpoint of Rejection Region) is z* = (c) The final conclusion is OA. The nicotine content is probably higher than advertised. B. There is not sufficient evidence to show that the ad is misleading.

A certain variable has a bell-shaped distribution with mean μ=176.16μ=176.16 and standard deviation σ=4.9σ=4.9. You observe a value of x=184x=184. Is this a TYPICAL value of the variable (within 2 standard deviations of the mean), or an UNUSUAL one (more than 2 standard deviations from the mean)?

The lifetime of a Michelin defender tire (in thousands of miles) is normally distributed with mean μ = 41 and standard deviation σ = 7. What proportion of Michelin tires have lifetimes between 35 and 47 thousand miles?