Using the Central Limit Theorem Answers

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 time needed for passengers to board the Twisting Thunder roller coaster is skewed right with a mean of 49 seconds and a standard deviation of 7.1 seconds. The time to board the Spiral Wonder roller coaster is skewed left with a mean of 44.8 seconds and a standard deviation of 3.7 seconds. What is the probability in a random sample of 32 times loading Twisting Thunder and 36 times loading Spiral Wonder that the mean time for Twisting Thunder is less than that of Spiral Wonder?

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?

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?

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 total number of forks dropped by customers per day at a busy restaurant is multimodal with a mean of 24.5 and a standard deviation of 3.3. If a random sample of 80 days is selected, what is the probability that the mean number of forks dropped during those days will be more than 25?

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 volume of liquid soap in containers labeled as 7 oz is approximately Normally distributed and has a mean of 7.15 oz and a standard deviation of 0.11 oz. If 8 bottles of the soap are randomly selected, what is the probability that the mean is less than 7.11 oz?

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?

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?