7) There are eight nickels and eight dimes in your pocket. You randomly pick a coin out of your pocket and place it on a counter. Then you randomly pick another coin. Both coins are nickels.

One card is selected at random from a deck of cards. Determine the probability of selecting a card that is less than 8 or a heart. Note that the ace is considered a low card. The probability that the card selected is less than 8 or a heart is (Type an integer or a simplified fraction.)

The PMF of a random varlable \( X \) taking value in \( N \cup\{0\} \) is given by \( P_{I}(i)=e^{-\lambda} \frac{\lambda^{i}}{n}, i=0,1,2, \ldots \) where \( \lambda \) is a positive real number. Given that \( \lambda=2 \), find \( P(X=0) \) \( P(X>2) \)

A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with three different members. There are 15 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below. a. How many different ways can the four officers be appointed? There are \( \square \) different ways to appoint the four officers. b. How many different ways can a committee of three be appointed? There are \( \square \) different ways to appoint a committee of three. c. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates? P(getting the three youngest of the qualified candidates) = (Type an integer or a simplified fraction.)

(b) If an output component is only accepted when its length lies in the range between 112.8 mm and 168.0 mm , find the expected proportion of components that are accepted. i.e. determine the below probability. Enter your answer rounded correct to 4 decimal places \( P(112.8<X<168.0)= \) Number mm

Dr Faridon Amdjadi, Mechanical Engineerin Find the probability \( P(-1.15<z<0.09) \) using the standard normal distribution. Select the correct answer. 0.5894