Can you please show me step by step. I\'d like to understand how to get the answ
ID: 2922872 • Letter: C
Question
Can you please show me step by step. I'd like to understand how to get the answer. Also I'm using a TI-30XA Calculator
13% of individuals insured by All-Driver Automobile Insurance Company have received at least one traffic ticket. (See exercise 49 on page 339 of your textbook for a similar problem.) Question 2 For a sample of 145 insured individuals, what is the probability that between 13 and 26 of them have received at least one ticket? The hotel room rate in New York City is normally distributed with a mean of $286 per night. Assume that the standard deviation is unknown. (See exercise 25 on page 289 of your textbook for a similar problem.) Question 3 If 25% of the New York City hotel room rates are more than $303 per night, what is the variance? (Remember the label.) On the SAT, the average Writing score is 467 points and the average Mathematics score is 538 points. The standard deviation is 76 points on each part of the test. Now suppose 42 test takers are selected. See exercise 21 on page 326 of your textbook for a similar problem.) Question 4 93% of the time the sample average writing score should be less than what? (Remember the label.)Explanation / Answer
Question 2:
p = 0.13
n = 145
P(13 < X < 26) = P(X <= 26) - P(X <= 13)
P(X <= 26) this can be found using binomial distribution formula
P(X <= 26) = 0.97 (excel formula to solve this: =BINOM.DIST(26,145,0.13,TRUE))
P(X <= 13) = 0.09 (excel formula to solve this: =BINOM.DIST(13,145,0.13,TRUE))
P(13 < X < 26) = 0.97 - 0.09 = 0.88
Question 3:
mean = 286, x = 303
P(X > x) = 0.25
Respective z-value = 0.67
Using Central limit theorem
z = (x - mu)/sigma
sigma = (303 - 286)/0.67 = 25.37
Quetion 4:
mean = 467, std. dev. = 76
n = 42
For 93% i.e. 0.07 area on the right, respective z-value = 1.48
x = mean + z*sigma/sqrt(n) = 467 + 1.48*76/sqrt(42) = 484.36