Question

In: Statistics and Probability

Heights for preschool aged students are approximately normally distributed with a mean of 40 inches and...

Heights for preschool aged students are approximately normally distributed with a mean of 40 inches and a standard deviation of 2.3. Lilly is a preschool student who is 43.5 inches tall.

A. Using the empirical rule, what percent of preschool aged students are between 37.7 inches tall and 46.9 inches tall? Do not round your answer. Make sure your answer includes a percent sign. 93.57%

B. Using the standard normal distribution table, what proportion of preschool aged students are shorter than Lilly? Do not round your answer from the table. .68

C. Using the standard normal distribution table, what proportion of preschool aged students are taller than Lilly? Do not round your answer from the table.

D. Sophie is also a preschool aged student. Her doctor tells her parents that Sophie's height is in the 23rd percentile. What is Sophie's height? Do not round your answer.

Solutions

Expert Solution


Related Solutions

The heights of males in a population are approximately normally distributed with mean 69.2 inches and...
The heights of males in a population are approximately normally distributed with mean 69.2 inches and standard deviation 2.92. The heights of females in the same population are approximately normally distributed with mean 64.1 inches and standard deviation 2.75. a. Suppose one male from this age group is selected at random and one female is independently selected at random and their heights added. Find the mean and standard error of the sampling distribution of this sum. Mean = Standard deviation...
6. Heights in inches for American males aged 20 and over are approximately normally distributed (symmetric)...
6. Heights in inches for American males aged 20 and over are approximately normally distributed (symmetric) with the mean height 69.3 inches and std deviation 2.99 inches. a.What percentage of American males in the above age group who are 6 feet or taller? b.Find the 99th percentile of the American males in the above age group and interpret it. c. Suppose a random sample of 100 American males aged 20 or more is taken, what is the probability that the...
The heights of 1000 students are approximately normally distributed with a mean of 174.5centimeters and a...
The heights of 1000 students are approximately normally distributed with a mean of 174.5centimeters and a standard deviation of 6.9 centimeters. Suppose 200 random samples ofsize 25 are drawn from this population and the means recorded to the nearest tenth of acentimeter. Determine (a) the mean and standard deviation of the sampling distribution of ̄X; (b) the number of sample means that fall between 171 and 177 cm . Let X be a random variable following a continuous uniform distribution...
The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and...
The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and standard deviation is unknown. Suppose 200 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter. with n=6 and assume the true σ is unknown and S=7.5 centimeters instead Determine (a) the mean and standard deviation of the sampling distribution of ¯X ; (b) the number of sample means that fall between 172.5...
The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and...
The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 7.9 centimeters. Suppose 200 random samples of size 35 are drawn from this population and the means recorded to the nearest tenth of a centimeter. Determine (a) the mean and standard deviation of the sampling distribution of X ; (b) the number of sample means that falls between 172.5 and 175.8 centimeters inclusive; (c) the number of sample means falling...
The heights of 18-year-old men are approximately normally distributed with a mean of 68 inches and...
The heights of 18-year-old men are approximately normally distributed with a mean of 68 inches and a standard deviation of 3 inches. (a) What is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? (b) For a sample of 36 18-year-old men, what is the probability that the average of their heights is between 67 and 69 inches?
Students' heights from Dorm A are normally distributed with a mean of 69.4 inches and standard...
Students' heights from Dorm A are normally distributed with a mean of 69.4 inches and standard deviation of 1.8 inches. Students heights from Dorm B are normally distributed with a mean of 71.6 inches and standard deviation of 1.7 inches. (You may consider these all to be population data.) A student is selected from one of the two dorms, but you don't know which one. At least how tall would that student need to be to have a probability of...
The heights of UNC sophomores are approximately normally distributed. The heights in inches of 8 randomly...
The heights of UNC sophomores are approximately normally distributed. The heights in inches of 8 randomly selected sophomores are shown below. Use these heights to find a 95% confidence interval for the average height μ of UNC sophomores. Give the endpoints of your interval to one decimal place. 72, 69, 70, 68, 70, 66, 75, 64 a) Use these heights to find a 95% confidence interval for the average height μ of UNC sophomores. Give the endpoints of your interval...
8.The heights of 18 year old men are approximately normally distributed, with mean 68 inches and...
8.The heights of 18 year old men are approximately normally distributed, with mean 68 inches and standard deviation 3 inches. If a random sample of nine 18 year old men is selected, what is the probability that the mean height ?̅ is between 67 and 69 inches? ___________________ 9. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. 95 173 129 95 75 94 116 100 85 ?̅ = 106.9 ??? ? =...
The cholesterol levels of women aged 21-40 in Canada are approximately Normally distributed with a mean...
The cholesterol levels of women aged 21-40 in Canada are approximately Normally distributed with a mean of 190 miligrams per decilitre (mg/dl). In July of 2007, a clinical assessment applied in Toronto to random sample of twenty–nine Asian female immigrants aged 21-40 had a mean level of 179.52 mg/dl and a standard deviation of 38 mg/dl. (a) At the 10% level of significance test whether the mean cholesterol level of Asian women is the same as the national average. (b)...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT