Homework #4 Solution Daily amount of raining in winter at Gaza is by ml cube, A random variable X have a continuous uniform distribution with A = 100 ml cube, B = 170 ml cube. Find the probability that a given day the amount of raining is:

Homework #4 Solution At most 110 ml cube. A= 100, B = 170 At most 110

Homework #4 Solution 1.More than 120 ml cube but less than 160 ml cube.

Homework #4 Solution At least 145

Homework #4 Solution A given normal distribution finds the value of k such: 1.P( z < k) = From table k = P( z > k) = P(z > k ) = = Then k = 2.33

Homework #4 Solution A given normal distribution finds the value of k such: 3. P( < z <k ) = Area left of z = = Then = 1 = k K = t 15,0.02 = k k = 2.249

Homework #4 Solution 9 basketball players through balls into a ring if the probability to score is 0.4 find: At least 4 players are scored n= 9, p = 0.4, q = 0.6

Homework #4 Solution At least 4 players are scored = 1-P(0)+P(1)+P(2)+P(3) =1- ( ) = 0.518

Homework #4 Solution At least 5 players failed to score p=0.6, q=0.4, At least 5 players failed to score = 1 – (P(0)+P(1)+P(2)+P(3)+P(4)

Homework #4 Solution At least 5 players failed to score = 1 – (P(0)+P(1)+P(2)+P(3)+P(4) = [ 1 – ( )]= Exactly 6 players are scored

Homework #4 Solution An experiment was run to test many of thermometers to test the freezing point of water. Assume that the mean reading is 0 c and the standard deviation is 1.1 c and assume that the readings are normal distribution. If one thermometer selected randomly find:

Homework #4 Solution 1.The reading of freezing point is less than 1.58 c. Then the area is , which is the probability of reading less than 1.58.

Homework #4 Solution The reading of freezing point is above c. Above -1.19

Homework #4 Solution The reading of freezing point is between 1.6c and -1.2c. Area = =

Homework #4 Solution A fabric manufacturer believes that the proportion of orders for row material arriving late is P=0.62. If random sample of 50 orders show that 4 or fewer arrived late, the hypothesis that P=0.62 should be rejected in favor of the alternative p < 0.62, use binomial distribution: 1.Find the probability of committing a type I error.

Homework #4 Solution

Find the probability of committing type II error for alternatives p=0.29, p=0.38, p=0.48

Homework #4 Solution

The average height of girls in a class at past year was cm with standard deviation of 6.9cm. If random sample of 20 girls were selected test the claim that the average height are cm at alpha = H 0 : µ=165.5 H a : µ≠165.5

Homework #4 Solution Calculated t Tabulated t Calculated t < tabulated t then We cannot reject the H 0

Homework #4 Solution State the regression equation with suitable hypothesis and calculate errors for : y x

Homework #4 Solution

N = 7; (∑X)2 = 5243; (∑X) (∑Y) = 7926 ;

Homework #4 Solution

For b 0 For b 1 Then it’s affected on model

Homework #4 Solution Then it’s affected on model Then the model is: