Using the Central Limit Theorem Answers

A course for a snail race has times that are skewed right with a mean of 5.18 minutes and a standard deviation of 2.34 minutes. If a random sample of 38 snails is selected, what is the probability that the mean race time is less than 4.3 minutes?

Chris makes a smoothie for breakfast every day. When he makes smoothies with bananas, the distribution of calories is skewed right with a mean of 248.6 and a standard deviation of 39.1. His berry smoothies have a distribution of calories that is approximately Normal with a mean of 279.1 calories and a standard deviation of 60.8. Random samples of 35 of each type of smoothie are selected. What is the probability of the banana smoothies having fewer mean calories than the berry smoothies?

The cost to produce a batch of granola bars is approximately Normally distributed with a mean of $7.19 and a standard deviation of $0.86. If a random sample of 12 batches of granola bars is selected, what is the probability that the mean cost will be more than $7.00?

The heights of a species of plant are approximately Normally distributed, have a mean of 9.31 cm, and have a standard deviation of 0.55 cm. If 20 of the plants are randomly selected, what is the probability that the mean plant height is less than 9.5 cm?

The distribution of the number of blocks a young child can stack before their tower falls is approximately Normally distributed with a mean of 12.7 blocks and a standard deviation of 1.4 blocks. If 6 of the child’s towers are randomly selected, what is the probability that the mean number of blocks is more than 11 blocks?

The number of marshmallows an adult can fit in their mouth is skewed right with a mean of 6.5 and a standard deviation of 0.58. What is the probability that a random sample of 40 adults would have a mean of at least 7 marshmallows?

The monthly cost for cell phones for plan Amazing has a mean of $39.17 with a standard deviation of $13.58, while the monthly cost for plan Best has a mean cost of $41.16 with a standard deviation of $7.18. A random sample of 37 phones is selected from plan Amazing, and a random sample of 40 phones is selected from plan Best. What is the probability that the mean cost for plan Amazing will be more than the mean cost for plan Best?

The number of pieces of cat food in a one-cup scoop is approximately Normally distributed with a mean of 344 pieces and a standard deviation of 16 pieces. If a random sample of 28 scoops of cat food is selected, what is the probability that the mean number of pieces will be more than 350 pieces?

The distribution of time spent brushing teeth for the 1,200 students in a school is multimodal with a mean of 43 seconds and a standard deviation of 8.99 seconds. If a random sample of 9 students is selected, is it appropriate to calculate the probability of the sample mean being less than 30 seconds using an approximately Normal model?

Libby earns a mean of 92.9 points with a standard deviation of 5.5 points in her math classes and a mean of 90.3 with a standard deviation of 6.1 points in her history classes. Both distributions are skewed left. If a sample of 30 of her math scores and 31 of her history scores is randomly selected, what is the probability that her mean math score will be more than her mean history score?