A normally distributed population has a mean of and a standard deviation of . a. Determine the probability that a random sample of size selected from this population will have a sample mean less than . b. Determine the probability that a random sample of size selected from the population will have a sample mean greater than or equal to . a. . 0478

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.1. (round your answers to four decimal places.) (a) if the distribution is normal, what is the probability that the sample mean hardness for a random sample of 8 pins is at least 51?

Lems1. the following data set represents the scores on intelligence quotient(iq) examinations of 40 sixth-grade students at a particular school: 114, 122, 103, 118, 99, 105, 134, 125, 117, 106, 109, 104, 111, 127,133, 111, 117, 103, 120, 98, 100, 130, 141, 119, 128, 106, 109, 115,113, 121, 100, 130, 125, 117, 119, 113, 104, 108, 110, 102(a) present this data set in a frequency histogram.(b) which class interval contains the greatest number of data values? (c) is there a roughly equal number of data in each class interval? (d) does the histogram appear to be approximately symmetric? if so,about which interval is it approximately symmetric?

What is the value of the discriminant of the quadratic equation -2x = -8x + 8 and what does its value mean about thenumber of real number solutions the equation has?