The undergraduate grade point averages​ (UGPA) of students taking an admissions test in a recent year can be approximated by a normal​ distribution, as shown in the figure.   ​(a) What is the minimum UGPA that would still place a student in the top 10​% of​ UGPAs? ​(b) Between what two values does the middle 50​% of the UGPAs​ lie?               3.2642.52Grade point average μ=3.26 σ=0.16 x

Exercise 2: Finding the Area Under the Curve In Major League Baseball, the average fastball pitch is 90 miles per hour, μ = 90, with a standard deviation of 3 miles per hour, σ = 3. A pitcher’s fastball is 96 miles per hour. Is he among the fastest 1 percent of pitchers?     A pitcher’s fastball is 95 miles per hour. Is he among the fastest 2.5 percent of pitchers?     A pitcher’s fastball is 85 miles per hour. Is he among the slowest 2.5 percent of pitchers?     A pitcher’s fastball is 80 miles per hour. Is he among the slowest 1 percent of pitchers?   Use Assignment05_Data.xlsx to solve these problems. Or, you may use the Area Under the Curve Table and a handheld calculator. The key part of your solution is used the correct z-value. Remember: z-values can be positive or negative. The Area Under the Curve Table only shows positive z-values. Because the normal curve is symmetrical, the probability of negative z-values are the same has their corresponding…

IQ scores form a normal distribution with a mean of μ =25 and a standard deviation of   σ = 12. Find the z-score for X= 30 and a sample of n = 89 people?

Consider the normal distribution represented by the normal curve in the figure to the right. (Assume the two labeled values are equidistant from the mean.) Complete parts (a) and (b) below. 95% of the data 73.2 cm 96.8 cm (a) Find the mean μ and standard deviation σ of the distribution. με cm (Simplify your answer.) σ = cm (Simplify your answer.) (b) Find the first quartile Q1 and the third quartile Q3 of the distribution. ༠ ༤ cm (Round to the nearest tenth as needed.) Q3≈ cm (Round to the nearest tenth as needed.)

The per capita energy consumption level (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal distribution, as shown in the figure. (a) What consumption level represents the 5th percentile? (b) What consumption level represents the 22nd percentile? (c) What consumption level represents the third quartile? u= 2309 kWh o = 571.7 kWh E 309 2309 4309 Kilowatt-hours (a) The consumption level that represents the 5th percentile is kilowatt-hours. (Round to the nearest integer as needed.) (b) The consumption level that represents the 22nd percentile is kilowatt-hours. (Round to the nearest integer as needed.) (c) The consumption level that represents the third quartile is kilowatt-hours. (Round to the nearest integer as needed.)

Find the z score

Interstate Speeds It has been reported that the standard deviation of the speeds of drivers on Interstate 75 near Findlay, Ohio, is 8 miles per hour for all vehicles. A driver feels from experience that this is very low. A survey is conducted, and for 29 drivers the standard deviation is 9.1 miles per hour. At =α0.05, is the driver correct? Assume the variable is normally distributed.  (a)State the hypotheses and identify the claim with the correct hypothesis.

Solve for C

In the normal distribution (the area under the normal curve): The area (at and) below the mean (z = 0.00) is % ___.  of the area. The area between z = -1.00 and z = +1.00 is approximately ____.  % of the area. The area between z = +1.00 and z = +2.00 is approximately  _____. % of the area. The area between z = -2.00 and z = +2.00 is approximately  ____ % of the area.