Alazy high school senior types up application and envelopes to and different colleges, but puts the applications randomly into the envelopes. what is the expected number of applications that went to the right college?

Complete Question:

A lazy high school senior types up application and envelopes to n different colleges, but puts the applications randomly into the envelopes. What is the expected number of applications that went to the right college?

The expected number is 1

Step-by-step explanation:

In order to get a better understanding of the answer above let explain some terms

Expected Number (Value) :

The expected value (EV) is an anticipated value for an event.In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.

The basic expected value formula is the probability of an event multiplied by the amount of times the event happens: (P(x) * n).

from the formula P(x) is likelihood that application would reach the right college = 1/n

and n = is the number of applications

hence the expected number of application = = 1

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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