Question

For three problems listed below determine the following :

(1) what type of probability distribution would be used to solve each problem and why;

(2) pick one problem only from below and provide a detailed solution with an explanation;

(3) indicate which problem you selected to solve in your subject line

i. The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. Find and interpret the probability that a randomly selected sixth-grade student reads less than 100 words per minute. i. A Wendy's manager performed a study to determine a probability distribution for the number of people, X, waiting in a line during lunch. The results were as follows. Find and interpret the probability that 10 or more people are waiting in line for lunch? Probability P(x) xP(x) 0 0.011 7 0.098 1 0.035 0.063 2 0.089 0.035 9 3 0.150 10 0.019 4 0.186 11 0.004 5 0.172 12 0.006 6 0.132 i. Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. As random sample of 20 Clarinex-D users is obtained, and the number of patients who experienced insomnia is recorded. Find and interpret probability that 3 or fewer experienced insomnia as a side effect.

Answer 1

(i) Let X is the random variable denotes the number of words read by student per minute.

Given

X ~ N( 125 , 24² )

We have to find the probability that a randomly selected sixth grade student reads less than 100 words per minute.

i.e. P(X < 100 )

we can compute this probability by converting it into z-score and then using the standard normal distribution table.

X- 100 P(X < 100) P

  

100 125 PZ< 24

  

= P (Z 1.0417)

  

=1 P(Z 1.0417)

  

=1-0.8508

0.1492

0.03 Z 0.00 0.01 0.02 0.04 0.05 0.06 0.07 0.08 0.09 0.504 0.0 0.5 0.508 0.512 0.516 0.51990.5239 0.5279 0.5319 0.5359 0.5398 0.5438 0.5478 0.55170.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.2 0.5793 0.5832 0.5871 0.591 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.67 0.6736 0.67720.6808 0.6844 0.6879 0.5 0.6915 0.695 0.6985 0.7019 0.70540.7088 0.7123 0.7157 0.719 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.758 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.791 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.834 0.8365 0.8389 0.8413 0.8438 0.8461 0.8485 0.85080.8531 0.8554 0.8577 0.8599 0.8621 1.0 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.877 0.879 0.881 0.883 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.898 0.8997 0.9015 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.91470.9162 0.9177 1.3 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.937 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2,0