Given a normal distribution with μ = 30 and o=6, find (a) the normal curve area to the right of x = 16; (b) the normal curve area to the left of x = 22; (c) the normal curve area between x = 32 and x = 40; (d) the value of x that has 80% of the normal curve area to the left; and (e) the two values of x that contain the middle 70% of the normal curve area.

The heights of 1500 students are normally distributed with a mean of 166.5 centimeters and a standard deviation of 7.9 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would be expected to have heights (a) less than 151.0 centimeters? (b) between 161.5 and 175.0 centimeters inclusive? (c) equal to 168.0 centimeters? (d) greater than or equal to 181.0 centimeters? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table.

A normal distribution has a mean of u= 80 with o= 12. Find the following proportions with the given score: (X < 74). Be sure to illustrate the normal distribution and shade in the region in question.

The data represents the daily rainfall​ (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. Does the frequency distribution appear to be roughly a normal​ distribution?

​(a) The figure to the right represents the normal curve with μ=266 days and σ=16 days. The area to the left of X=245 is 0.0947. Provide two interpretations of this area.   Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Type integers or​ decimals.)   A. The proportion of human pregnancies that last more than nothing days is nothing.   B. The proportion of human pregnancies that last less than nothing days is nothing.