8. LetZ be a standard normal random variable. determine the value of c .P(-c < Z c) = 0.10 . Round your answer to at

8. LetZ be a standard normal random variable. determine the value of c .P(-c < Z <) = 0.9109

Round your answer to two decimal places.

9. Suppose that the times taken for germination for cauliflower seeds are normally distributed with a mean of 7.1 days. Suppose also that exactly90 % of the cauliflower seeds germinate indays 6 or more. Find the standard deviation of times taken for germination for cauliflower seeds. Round your answer to at least two decimal places.____days.

10. Suppose that the antenna lengths of woodlice are approximately normally distributed with a mean of 0.2 inches and a standard deviation of 0.05inches. What proportion of woodlice have antenna lengths that are at least 0.15 inches? Round your answer to at least four decimal places.

11. A soft drink company has recently received customer complaints about its one-liter-sized soft drink products. Customers have been claiming that the one-liter-sized products contain less than one liter of soft drink. The company has decided to investigate the problem. According to the company records, when there is no malfunctioning in the beverage dispensing unit, the bottles contain 1.015 liters of beverage on average, with a standard deviation of 0.14 liters. A sample of 60bottles has been taken to be measured from the beverage dispensing lot. The mean amount of beverage in these 60 bottles was 0.993liters. Find the probability of observing a sample mean of0.993 liters or less in a sample of60 bottles, if the beverage dispensing unit functions properly.

Round your answer to at least three decimal places.

13. A psychologist is interested in the mean IQ score of a given group of children. It is known that the IQ scores of the group have a standard deviation of 13. The psychologist randomly selects 70children from this group and finds that their mean IQ score is 98. Based on this sample, find a 95% confidence interval for the true mean IQ score for all children of this group. Then give its lower limit and upper limit.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

Lower limit:

Upper limit:

14. (a)Consider a t distribution with 17 degrees of freedom. ComputeP(-1.71 < t < 1.71). Round your answer to at least three decimal places.

P(-1.71 < t < 1.71) = ___.

(b)Consider a t distribution with7 degrees of freedom. Find the value of c such that P(t > c) = 0.10 . Round your answer to at least three decimal places.C = ___