ucisity 16F X? Sketch a graph of the density function. Indicate on this graph the probability that X lies between 1.1 and 1.9. Find this probability. (b) Find the probability that a randomly selected sample of Pima clay loam will have bulk density less than .9 g/cm³. (c) Would you be surprised if a randomly selected sample of this type of soil has a bulk density in excess of 2.0 g/cm3? Explain, based on the probabil- ity of this occurring. (d) What point has the property that only 10% of the soil samples have bulk density this high or higher? (e) What is the moment generating function for X? 41. Most galaxies take the form of a flattened disc, with the major part of the light coming from this very thin fundamental plane. The degree of flattening differs from galaxy to galaxy. In the Milky Way Galaxy most gases are concentrated near the center of the fundamental plane. Let X denote the perpendicular dis- tance from this center to a gaseous mass. X is normally distributed with mean 2.29 СИ exm Tainy/SlaTCS Taiatk 5-18,23 rotabiinteSteISHCS abilit Woudr 4.5 36 00 and standard deviation 100 parsecs. (A parsec is equal to approximately 19.2 iw trillion miles.) 146 INTRODUCTION TO PROBABILITY AND STATISTICS (a) Sketch a graph of the density for X. Indicate on this graph the probability that a gaseous mass is located within 200 parsecs of the center of the fun- damental plane. Find this probability. geri.co.ck lidedong srls bom (b) Approximately what percentage of the gaseous masses are located more than 250 parsecs from the center of the plane? (c) What distance has the property that 20% of the gaseous masses are at least this far from the fundamental plane?t (d) What is the moment generating function for X?. 42. JAmong diabetics, the fasting blood glucose level X may be assumed to be ap-

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.