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- Assume the random variable x is normally distributed with mean p= 89 and standard deviation o = 5. Find the indicated probability. P(75According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 6666 inches and a standard deviation of 2.52.5 inches. Suppose one Asian adult male is randomly chosen. Let X=X= height of the individual. (a) State the distribution of XX. X∼NX∼N (( , )) (b) Find the probability that the person is between 6464 and 6969 inches.Select the correct graph for the situation with shading for the region corresponding to the probability. Round your answer to four decimal places, if necessary.The probability that the person is between 6464 and 6969 inches is . (c) Would you expect to meet many Asian adult males over 7474 inches? Explain why or why not, and justify your answer numerically. Yes, the probability that an Asian male is over 7474 inches tall is 0.00070.0007. Yes, the probability that an Asian male is over 7474 inches tall is 0.99930.9993.…3.- It has been found that the waiting time to obtain a table in a cafe during rush hour has a normal distribution with a mean of 130.7 min. and a standard deviation of 12.5 min. How long do people have to wait to be given a table with the following probability?a) P (X ≥ Xo) = 0.83.b) P (X ≥ Xo) = 0.12c) P (X ≤ Xo) = 0.92d) P (X ≤ Xo) = 0.07Let the r.v. Z have the standard normal distribution. Find (i) P(Z≤-2.15) (ii) P (Z≥ 1.96) (iii) P (-1.96≤ ? ≤ −0.84) (iv) P (-1.30≤ ? ≤ 2.18) (v) P (0≤ ? ≤ 1.20)Let x denote the IQ of an individual selected at random from a certain population. The value of x must be a whole number. Suppose that the distribution of x can be approximated by a normal distribution with mean value 100 and standard deviation 15. Approximate the following probabilities. (b) P(x ≤ 130) (c) P(x < 130) (Hint: x < 130 is the same as x ≤ 129.)Assume the random variable x is normally distributed with mean µ = 88 and standard deviation o = 4. Find the indicated probability. P(78The average amount of money spent for lunch per person in the college cafeteria is $6.06 and the standard deviation is $2.82. Suppose that 41 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. What is the distribution of X? X ~ N( , ) What is the distribution of x¯? x¯ ~ N( , ) For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.32 and $6.63. For the group of 41 patrons, find the probability that the average lunch cost is between $6.32 and $6.63. For part d), is the assumption that the distribution is normal necessary? YesNoThe average amount of money spent for lunch per person in the college cafeteria is $7.11 and the standard deviation is $2.1. Suppose that 42 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.What is the distribution of XX? XX~ N(,) What is the distribution of ¯xx¯? ¯xx¯~ N(,) For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $7.294 and $7.636. For the group of 42 patrons, find the probability that the average lunch cost is between $7.294 and $7.636. For part d), is the assumption that the distribution is normal necessary? Yes or NoAssume the random variable x is normally distributed with mean μ=8585 and standard deviation σ=44. Find the indicated probability. P(x<77)A random variable follows the continuous uniform distribution between 10 and 210. a. Calculate the following probabilities for the distribution. 1. P(75 sxs 85) 2. P(40The average amount of money spent for lunch per person in the college cafeteria is $6.28 and the standard deviation is $2.92. Suppose that 8 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal placeswhere possible. What is the distribution of XX? XX~ N(,) What is the distribution of ¯xx¯? ¯xx¯~ N(,) For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $4.74 and $5.38. For the group of 8 patrons, find the probability that the average lunch cost is between $4.74 and $5.38. For part d), is the assumption that the distribution is normal necessary? NoYes1*SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON