Given that the mean of 15 bowlers that have been selected at random is distributed normally with mean 157 and std dev of 12 The probability that a random sample of 15 bowlers would have an average score greater than 165 will be: mean=157 std dev,σ =12 std error=σ/√n=12/√15=3.0984 standardizing xbar to z=(xbar-μ)/(σ/√n) P(xbar>165)=P(165-157)/3.0984 =P(z>2.582) using normal probability tables we get: P(z>2.582)=0.0049
Next we calculate the probability that a random sample of 150 bowlers will have an average score greater than 165. μ=157 σ=12 std error=12/√150=0.9797=0/98 standardizing the xbar we get: z=(165-157)/0.98 =P(z>8.165) from normal table this will give us: P(z>8.165)=0.00
