Normal Distributions

Assume that the scores on a certain test are normally distributed with a mean of 100 and a standard deviation of 15. What is the z-score for a score of 130?

A company manufactures light bulbs which have a mean life of 5000 hours and a standard deviation of 100 hours. The life length of these light bulbs follows a normal distribution. What is the probability that a light bulb will have a life length of less than 4800 hours?

Suppose $Z$ follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) $P(Z>1.55)=$ (b) $P(Z \leq 1.48)=$ (c) $P(-0.46<\mathrm{Z}<1.71)=$

In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.1 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than 67 inches tall is (Round to four decimal places as needed) (b) Find the probability that a study participant has a height that is between 67 and 72 inches. The probability that the study participant selected at random is betwe (Round to four decimal places as needed) (c) Find the probability that a study participant has a height that is more than 72 inches. The probability that the study participant selected at random is more than 72 inches tall is (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. The events in parts (a) and (c) are unusual because its probabilities are less than 0.05 . B. There are no unusual events because all the probabilities are greater than 0.05 . C. The event in part (a) is unusual because its probability is less than 0.05 .

The weights of a certain dog breed are approximately normally distributed with a mean of $\mu=51$ pounds, and a standard deviation of $\sigma=7$ pounds. A dog of this breed weighs 45 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed. \[ z=\square \text { o } \] A dog has a z-score of -0.57 . What is the dog's weight? Round your answer to the nearest tenth as needed. pounds A dog has a z-score of 0.57 . What is the dog's weight? Round your answer to the nearest tenth as needed. pounds

Find the value of $z_{\alpha}$. \[ \alpha=0.12 \] The value of $z_{0.12}$ is (Round to two decimal places as needed.)

A company claims that the average salary of its employees is $75,000. A random sample of 100 employees is taken and their average salary is found to be $72,000 with a standard deviation of $5000. Test the company's claim using a significance level of 0.05.