Georgianna claims that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons. We have a random sample of 20 children from the city, with a mean of 4.6 years of piano lessons and a standard deviation of 2.2 years. Required:Explicitly state and check all conditions necessary for inference on these data.

The  condition  are

           The  Null hypothesis is  

           The  Alternative hypothesis is  

The  check revealed that

             There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons

Step-by-step explanation:

From the question we are told that

     The  population mean is  

      The sample size is  n =  20

      The sample mean is  

       The  standard deviation is

   The  Null hypothesis is  

   The  Alternative hypothesis is  

So i will be making use of   level of significance to test this claim

    The critical value of   from the normal distribution table is  

Generally the test statistics is mathematically evaluated as

substituting values

Looking at the value of  t and we see that   so we fail to reject the null hypothesis  

  This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1