A data from a physician office shows that only 10% of patients are taller than 6 ft. If there are 4 patients in the office,find the probability that at least one of them is taller than 6 ft. Then, find mean and standard deviation of the number of patients taller than 6ft.

Sara is a big hip-hop music fan. Her friend Matt is a big rap music fan. They each have a huge library of songs in their digital music libraries. They each randomly sample 50 songs from their libraries and record the lengths of the songs selected. The average of the selected hip-hop songs was x1 = 245 seconds with a sample standard deviation of 4 seconds. The average of the selected rap songs was x2 = 275 seconds with a sample standard deviation of 6 seconds. They would like to know if the average length of hip-hop songs is different than the average length of rap songs. (a) What are the appropriate null and alternative hypotheses for this test? H0: ?1 − ?2 = 0 Ha: ?1 − ?2 ≠ 0 H0: ?1 − ?2 < 0 Ha: ?1 − ?2 > 0 H0: ?1 − ?2 = 0 Ha: ?1 − ?2 < 0 H0: ?1 − ?2 = 0 Ha: ?1 − ?2 > 0 (b) Calculate the test statistic. (Round your answer to two decimal places.) (c) Assume for purposes of this study, the degrees of freedom are 80. At a 5% significance level, what is the…

Nationally, the average score on the college entrance exams (verbal test) is 453 with a standard deviation of 95. A random sample of 152 freshmen entering St. Algebra College shows a mean score of 505. Is there a significant difference.