b. What is the probability that the sample mean will be below 0.95 centimeters?

c. Above what value do 2.5% of the sample means fall?

3. The amount of pyridoxine (in grams) per multiple vitamin is normallydistributed with µ = 110 grams and σ = 25 grams. A sample of 25 vitamins is tobe selected. a. What is the probability that the sample mean will be between 100 and 120grams?

b. What is the probability that the sample mean will be less than 100 grams?

c. What is the probability that the sample mean will be greater than 100 grams?

d. So, 95% of all sample means will be greater than how many grams?

e. So, the middle 70% of all sample means will fall between what two values?

4. The amount of time required for an oil and filter change on an automobile isnormally distributed with a mean of 45 minutes and a standard deviation of 10minutes. A random sample of 16 cars is selected. a. What would you expect the standard error of the mean to be?

b. What is the probability that the sample mean is between 45 and 52 minutes?

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c. What is the probability that the sample mean will be between 39 and 48minutes?

5. The amount of bleach a machine pours into bottles has a mean of 36 oz. with astandard deviation of 0.15 oz. Suppose we take a random sample of 36 bottlesfilled by this machine. a. The probability that the mean of the sample exceeds 36.01 oz. is __________.

b. The probability that the mean of the sample is less than 36.03 is __________.

c. The probability that the mean of the sample is between 35.94 and 36.06 oz. is__________.

d. The probability that the mean of the sample is between 35.95 and 35.98 oz. is__________.

e. So, 95% of the sample means based on samples of size 36 will be between__________ and __________.

6. To use the normal distribution to approximate the binomial distribution, weneed ____ and ____ to be at least 5.

7. T Assume that house prices in a neighborhood are normally distributed withstandard deviation $20,000. A random sample of 16 observations is taken. Whatis the probability that the sample mean differs from the population mean by morethan $5,000?

TABLE (A)Times spent studying by students in the week before final exams follow a normaldistribution with standard deviation 8 hours. A random sample of 4 students wastaken in order to estimate the mean study time for the population of all students.a. Referring to Table (A), what is the probability that the sample mean exceeds thepopulation mean by more than 2 hours?