**Educational Content on Understanding Standard Deviations and Z-Scores**For full credit, show your work. Include calculations and/or a sketch of the normal curve with area shaded. State whether you used the or the OLI Normal Calculator or the Empirical Rule or something else – if you used something else, say what it was so I can find it.**1) According to the WHO report, girls who are one month old have a mean head circumference of 36.55 centimeters with a standard deviation of 1.17 cm.**a) Ann is concerned that her daughter’s head is small. Her daughter has a head circumference of 34.25 centimeters when she is one month old. If we consider measurements more than 2 standard deviations from the mean as unusual, is Ann’s daughter’s head measurement unusually small? Support your answer.b) According to Medscape.com, microcephaly is a head circumference more than two standard deviations below the mean. What percentage of 1-month old girls will be categorized as having microcephaly? How do you know?**2) According to the WHO report, girls who are 2-years old have a mean head circumference of 47.18 cm with a standard deviation of 1.40 cm. A two-year-old girl with Down’s Syndrome has a head circumference of 44.5 cm. Children with Down’s Syndrome typically have smaller heads, so this is not surprising.**a) Relative to the WHO data, what is this girl’s z-score? What does the z-score tell us?b) Using the WHO data in a normal model, what percentage of the girls has a head circumference that is smaller than the girl with Down’s Syndrome?---**Notes:**- The content discusses calculating whether specific measurements are statistically unusual based on standard deviations.- Understanding z-scores involves determining how far a particular measurement is from the mean, expressed in terms of standard deviations.- The example considers normal distribution, which implies a bell-shaped curve where most data points fall within three standard deviations from the mean.- Using tools like the OLI Normal Calculator or relying on the Empirical Rule can assist in determining probabilities and unusual measurements.

NOTE: As per the guidelines, we are allowed to solve the first question only. Please repost other as separate questions. I will surely solve them! 1). a). We are given: Mean=μ=36.55Standard deviation=σ=1.17 It is said that if the value is beyond than 2 standard deviation, i.e, if the value is less than the lower limit or more than the upper limit of 2 standard deviation, it is considered as unusual.Now, we will calculate the limits of 2 standard deviation, i.e, μ±2σ. The limits are calculated as: μ-2σ=36.55-2*1.17 =34.2μ+2σ=36.55+2*1.17 =38.9 The limits of 2 standard deviation is (34.2,38.9).The given value is 34.25. As the given value lies within the limits of 2 standard deviation, it is not considered as unusual. Therefore, Ann's daughter's head measurement IS NOT unusually small. b). According to Empirical rule, 68% of the data values lies within 1 standard deviation limits, i.e, μ+σ 95% of the data values lies within 2 standard deviation limits, i.e, μ+2σ 99.7% of the data values lies within 3 standard deviation limits, i.e, μ+3σ Hence, we see that 5% of data lies outside the 2 standard deviation limits. This 5% is divided on both sides of the mean. In this case, we need to find the percentage of below mean part.Thus, in order to obtain the percentage of one side of mean, we divide 5% by 2, Required percentage=5%/2 =2.5% Therefore, 2.5% of 1-month old girls will be categorized as having microcephaly.