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- In a t distribution with 10 degrees of freedom, what is the probability of getting a value within two standard deviations of the mean?Suppose we have a normal distribution N(2, 4), using the Empirical rule, what proportion of data is between the data values -2 and 6?Suppose weights, in pounds, of dogs in a city have an unknown distribution with mean 31and standard deviation 5 pounds. A sample of size n=39 is randomly taken from the population and the sum is taken. What is the probability that the resulting sum is between 1180 and 1194 pounds?
- What is the value of t*, the critical value of the t distribution for a sample of size 22, such that the probability of being greater than t* or less than -t* is 1%? t* = 7.34. Suppose that 60% of college students own a smart phone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here?What happens to the t-distribution as the sample size increases?
- A random sample of n= 4 is obtained from a normal distribution μ=30, σ=8. What is the probability the sample mean will be smaller than M = 22? Report to the thousandthsAssume the random variable X is normally distributed with mean =50 and standard deviation =7. Compute the probability. P(X > 36)=5. What is the value of t, the critical value of the distribution with 8 degrees of freedom, which satisfies the condition that the probability is 0.10 of being larger than tᵒ? (a) 1.415 (b) 1.397 (c) 1.645 (d) 2.896 (e) 0.906.
- A normal distribution has a mean of u = 60 with o- 8. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 54?Suppose that the mean value of the interpupillary distance for all adult males is 65 mm, and the population standard deviation is 5 mm. If the distribution of interpupillary distance is normal and a sample of n=25 adult males is selected, what is the probability that the same average distance, x-bar, for these 25 scores will be between 64 and 67 mm? Same set-up as part a. More than 68 mm? Suppose that a sample of 100 adult males is obtained. Without assuming that interpupillary distance is normally distributed, what is the approximate probability that the average distance, x-bar, is between 64 and 67 mm? Same set-up as part c. More than 68 mm?Suppose weights, in pounds, of dogs in a city have an unknown distribution with mean 31 and standard deviation 5 pounds. A sample of size n=39 is randomly taken from the population and the sum is taken. What is the probability that the resulting sum is between 1180 and 1194 pounds?